How can I find carrots and potatoes in an older (pre-vegetable) minecraft world seed
Carrots and potatoes can only be reliably found in villages, and they must be generated after the crops were added into the game.
However, they are also a rare drop from zombies, and while it's not the fastest way to get the items, it will save you quite a bit of walking.
The easiest way to find potatoes and carrots is to defeat Zombies. They have a rare chance of dropping the new eats. You can also obtain them in newly generated villages, where they have a chance of spawning in place of wheat.
You can only find carrots and potatoes in a place where chunks have not loaded yet. If you have looked thousands of blocks, no carrots or potatoes will spawn there.
Carrots are also a rare drop from zombies and can be farmed normally.
There are two ways to get carrots and potatoes, but since your in an older world, the second way is modified a bit. Here's what they are:
Rare Drops from Zombies
In chunks that you haven't been in in the earlier verisons (before carrots and potatoes were added) there may be a village, which will have them.