Are there any drawbacks to mixing my armor?
I am wondering if it is okay to mix armors in the game? I mainly use heavy with a hood instead of a helmet but when doing Dark brotherhood missions I like to wear the light armor from them. Is that okay to do? Does anyone else do this? Do I need to spec into a certain armor type or can I continue to use both?
While it is perfectly fine to mix armor types, there are some elements in the game intented to make you identify with one type over the other.
Armor perks - Light armor perks only apply to light armor. Heavy armor perks only apply to heavy armor. Some perks farther up these trees require full four-piece sets (head, chest, hands, feet). If you are wearing armor pieces for armor rating - you'll probably get some of these perks. It's more point-efficient to focus on one tree instead of two.
Levels - when wearing mixed armor types, you'll get skill points toward both. These skill points can help you level faster. However, it's questionable whether these extra points help you survive fights better. You run a small risk of out-leveling your ability to survive (but there are many mechanisms in the game to counter this possibility).
Armorsmithing perks - These perks increase the amount of addition armor rating you get when improving your gear at the workbench. This additional armor can be very significant. It's more point-efficient to go up one side of the tree or the other. By choosing one side of the tree, you're choosing which armors you want to be better at improving.
To make a good armor selection decision, there is much to consider:
Consider the primary attributes of armor: armor rating and weight. Rating is why you want armor. It reduces physical damage taken. Weight is a big obstacle (less loot, less weapons, less potions). If you go without a helmet, you don't get armor rating from that slot. How much armor rating do you lose by that choice? Does the weight reduction (and magic bonus) make up for that? Can you compensate for the armor rating loss with an alteration spell?
Consider the secondary effects of armor: reduced movement, increased staggering, increased noise. Do you have ways to compensate for those problems? Are you prepared to trade away armor rating to solve those problems instead?
A good player can see the three paths (caster, light, heavy), see how the perks lead into those paths, and discern the tradeoffs when straying from those paths. It's fun to leave the obvious paths, but it's not fun to feel ineffective.
Skyrim is not a game you have to "win", esp. not on the first go-through in the first week after release. As the other answers indicate, there are many variables at work there and no one has played long enough to really say what's best or not, although the David B's answer is very good and demonstrates how experienced players can approach the mini-game of skill and perk selection.
My approach was to think about the character I wanted to try first: a warrior that can heal himself and can make potions, magic armor, and magic weapons. I chose to wear heavy armor because it seemed (after 1 hour) that making heavy armor was more lucrative. I've been happy with that choice. My next character will be totally different.
It seems like you like the light armor/robe approach but there is certainly nothing wrong with using heavy stuff if you think the situation warrants or just find a really great pair of dwarven gauntlets or whatever that will serve you well for at a few levels or until you can sell them.
Feeling ineffective is not fun, I agree, but there always the difficulty slider for those situations that just seem impossible. Save often.
Another observation: you don't have to spend your perk points right away or spend them on the things you think you do most. You can play for a good long while and then select perks based on what seems to be the most needful or interesting instead of what happens to open up.
Finally, if you do find yourself gimped in some fun-crushing way and you don't want to start afresh or from an early save, you can tweak almost everything about your character using the console commands. Yeah, you're meta-gaming, but it isn't like anyone is keeping score (Steam accomplishments notwithstanding).
Have fun and don't worry. Ohmi