Hi Kaliope -- welcome to NGA!
I personally wouldn't put those little seedlings into large pots right away... a 1-gallon pot would be more than plenty. I think your biggest issue is going to be lack of light during the winter; are you planning to use some type of grow light? If not, they may grow with the light from a south window, but not very well, I'm afraid.
On the bright side, you've been successful at starting those seeds, which is certainly the first step... I'd say go ahead and continue through the winter and see how your plant(s) does/do, then sometime in early to mid-March start some more seeds that you can pot up and put outdoors (or plant in the ground outdoors, if you have a garden). With the increasing sunlight during the spring and summer I think you will see a great difference in their growth -- and will likely harvest some nice peppers, too!
