This can be done with all pepper plants. :) I did this in a way myself this year. You can also do this with tomatoes.

Your pepper plants may still be establishing themselves after being removed from the ground and transplanted. For peppers to bear indoors, they do need lots of bright full spectrum light and some heat- but they will do fine and be healthy without bearing in a south facing sunny window for the year and will do well transplanted back into the garden in the spring when the weather warms.

Instead of removing the whole plant myself, I took cuttings and they've already rooted and been transplanted into containers. I have mine under lights and over heat mats with a fan on them now, which is where they'll stay until the spring. Some varieties will lightly bear down there, they have in the past (mostly the cayenne types for some reason). Cherry tomatoes will bear like this too sometimes although not abundantly.. at least not for me. But they do have a BIG jump on the season in the spring. This method makes it possible to grow those big, sweet, long season tomatoes that normally don't do well up north here. We have the heat but not enough days.

You can also do this with sweet potatoes. I took cuttings of spent vines and easily rooted them. I have them growing on in pots under lights too, like the peppers and tomatoes and some others.

I also tried rooting and growing on some mint this year to pick and put in tea over the cold winter months. Helps with stuffy noses and sore throats! This pineapple mint here is not only pretty in the window, but boy it's tasty in drinks and tea. I was able to root mint cuttings in Ball jars of water in a window and grow them on there- no bottom heat or light or anything needed.

Here is a link that might be useful: Pineapple Mint

It can be done, but I've always found them to lose vigor the following spring, compared to a new transplant. Maybe I'm doing something wrong though. Give it a try and let us know how it goes!

Personally I'd never bother overwintering anything that can be grown easily from seed. I plant my peppers anywhere from February to April and they do wonderfully.

I did really want to overwinter my Diascia this winter, because it was awesome but hard to start from seed. The cuttings didn't take though. Darn.

You have to be careful about not bringing pests in with your pepper plants. I tried extending my season with jalapenos and chilis last year and I had a hard time controlling the aphids. I ended up tossing the plants.