How to conquer counties with very low supply and many troops?
I'm playing a game now that started with Poland and has successfully created Lithuania and the Wendish Empire, so I can share what I learned works and doesn't work from hard experience.
The gist of the method is to win with battles, not sieges.
These counties have huge levies and very low supply limits, often with more levies and garrison defending a siege target than there are supply limits! Sieging such settlements is nearly impossible, since it takes so long due to the large force of defenders, and your own armies are suffering massive losses due to starvation. Eventually you simply don't have a large enough army to continue the siege, and that's assuming their allies haven't torn apart your siege force.
The strategy is to defeat their first big army head-on to get a good starting warscore, slowly grow warscore with harrying armies that are small enough to not suffer attrition, then besiege the target county to finish off your warscore.
The process usually looks like this:
Marshal one large army in a nearby county that has a high supply limit. Wait for full morale, and especially wait for the enemy to raise their armies! Those are your target.
Destroy their armies, starting with the largest and working down. You'll suffer supply attrition, but battles are fairly quick (quicker the larger your army) and the attrition losses will be few compared to trying to siege. You'll also get a very large warscore bump, around 30–40%.
Now split your big army (or armies, if your realm is very strong) into small harrying/hunting forces that fit within the typical supply limit of the surrounding counties. Keep these moving, so that the enemy can continue to raise levies. They'll raise pitiful armies of a few hundred down to a few single soldiers in most counties, which you can flatten quickly. This is to build up your warscore without suffering much (if any) supply limit attrition.
When they raise large levies (usually when you've been sitting in a county for a while [maybe due to a big battle] then move away, so their levies have had time to built up before raising), bring some of your harrying forces together into a large enough army again, smash them, then go back to harrying patrols. Keep those small armies moving.
As your harrying forces get worn down and smaller, combine them as necessary. By this time you'll know which patrol regions you need strong 1k armies and where you can get away with little 400-soldier forces. Just remember that your smaller armies will be tempting targets for the enemy. Watch their neighbourhoods closely.
When you have a decent warscore (my rule of thumb is that it's enough when they'd accept White Peace, but still won't accept Enforce Demands), then siege the county you're fighting over with all you've got. It will hopefully be pretty fast due to its depleted levies and your overwhelming army, so you can afford the supply limit attrition for just this one siege. One occupation should then put you to 100% warscore and you can Enforce Demands and take the county.
Profit!
The downside of this process is that the war(s) can take several years, since you're fighting a war of attrition on your terms instead of theirs. To do this, you need to have much more levies than your target and all their religious allies combined, and have a pretty stable and happy realm that will absorb opinion penalties from raised levies of up to about -20 or so.
The Pomeranian territory is a nice target because it's a small religious group (Slavic), so the allies are few. On the flip side it's usually held all by one Chief anyway, so you can only war every 10 years due to truces, making conquering Pomerania is quite slow.
Lithuania and Livonia are nice targets because there are so many different Chiefs that you can war on. That gives you more flexibility for your conquest strategy, and more opportunities for the Chiefs to suddenly find Jesus coincidentally during a Holy War on them. A ruler converting to Christianity is a pain because then the war ends without any county gains, but on the plus side now they're more susceptible to offers of vassalisation (assuming you make nice with them later and don't just forge claims on their titles), and their counties all suddenly have much better supply limits, giving you more maneuvering options when warring against the remaining pagans. They also won't be religious allies against you for the next Holy War you declare there.
Some miscellaneous bits of strategy that are good to keep in mind when waging this kind of war:
When using Holy War for [Region], declare war on all the neighbouring rulers within that region who also share a religion with your target. They're going to come fight you anyway, so you might as well get a county from each of them when you win! (If you don't think you can win, you're not ready to use the Holy War CB in that region.)
If you want to fight only one pagan, do it via forging claims. Pressing a claim will avoid them calling in all their religious neighbours, making it a much easier fight.
Don't underestimate the size of their first army. It will be huge compared to what you think those counties can raise. Use the Realm Size button in the ruler's screen to find out how many levies they can raise right now and in total, and make sure you do the same for all potential allies (which will vary depending on your Casus Belli). If you think you can smash that total, go for it.
Muster in a safe place, and lead with your largest levies. Don't worry if that makes it take longer, since this is a long style of war. If you just tell all your levies to meet on the border, make sure that tiny ones don't arrive first! Make sure that you aren't giving away any easy victories because you got your movements mixed up and exposed a small force to attack.
If you can, marry into some alliances nearby first. Good Christian rulers are very easy to convince to join your wars when they're against pagans. When you're halfway there and your armies are looking a little depleted, calling in an ally for the final siege can make all the difference.
Don't be afraid to hire mercenaries late in the war, for the same reason. You've probably not been spending any money because you've been at war for three years, so you probably have a decent treasury. Finish off the pagans with a fresh influx of 5,000 mercenaries!
Don't do this if you have any neighbours who want anything you've got, or if you have any rebellious vassals. They will see your realm levies are low and declare war on you, just when the end of your own war is starting to look within reach, and that sucks.
If you need mercenaries or allies right away to even think about starting the war, don't go to war. You won't last the length of time it takes to win this kind of war.
Get very good at managing marching time, using the hover-over tooltip for friendly and enemy armies. When you're trying to move a small harrying force away from a large levy that was suddenly raised, the difference between arriving at your destination right before that big army moves to the county it's in and right after can win or lose you the war! You don't want to give them any wins if you can help it, else the war will take forever.
Keep an eye on your warscore! Check it every few months or every year. If you ever notice it dropping when you haven't lost any recent battles, open up the war view and hover over the warscore. You'll notice an interesting negative (for you) entry that basically says "I still control the county!" This happen when wars drag on very long: if you don't control even one holding in the claimed county after a long time of warring, they start thinking that you'll never take it and they start gaining warscore (I've seen 35%!) from that. On the plus side, this means that they're ripe for the siege! You should be able to take one holding easily, and that will eliminate this "confidence" warscore completely and give you a big occupation bonus, which will likely get you to 100% and end the war.
I've had brutal campaigns in Scandinavia with huge losses of troops. From that experience I found the best tactic was to accept a lot of losses and go for quick wars by taking their holdings quickly with assaults.
You will get 100% warscore if you siege down all their holdings. Often the gavelkind will mean a lot of small kingdoms with one or two counties. If you land a massive stack of troops and initiate an assault as soon as possible you can take the whole lot before attrition ticks too much.
As soon as the primary holding is taken move your fleet into port to be ready to scoop up the army to minimise their time on the ground. Often even when you take the county it can't hold a lot of troops.
This will hit your levies hard so consider the following:
Check the fort level before attacking. The lower the fort level the better.
Typically a 10:1 ratio or more will go your way. Fort level affects
this a lot.Attack in summer. The winter conditions will add a huge negative
modifier to your attrition rate whereas coastal provinces in summer
can have attrition below 5%. You can feasibly siege down holdings
with a large garrison and a high fort rating or at least deplete them a lot then land the bulk of your army for the assault.In general you will lose a lot of men doing this but you can win
large wars in a single campaign season if you prepare properly.
Always get everything in place and make sure you time everything to
coincide with the start of summer (~June in Scandinavia).