For two years now, I've been playing around to see how little I could get away with on over-wintering pepper plants.
I've come to at least two conclusions.
First, yeah, it's best to uproot them and put them in fresh soil. I'm sure a master gardener can work around this, but the easiest way is to pluck them out, and put in fresh soil.
Second, there's pro's and con's to over-wintering. If you do it right, you'll get a good crop the next year (especially if you started too late to get any reasonable crop out of the year before). But, you're highly likely to be over-wintering the pests as well as the peppers. Speaking personally, the aphids seemed to greatly appreciate the warmth and care I bestowed on my over-wintered peppers. I suspect I'm lucky that, so far, it's only been aphids.
And, at the end of the year, the crop you get out of starting from seed (if done correctly) will have you wondering if over-wintering gets you more peppers. You'll get more peppers early from the over-winter, but the final tally is often a toss-up.