Do you have a sun porch or a very bright south facing window? It is possible to bring one indoors in winter, but without very bright conditions they will tend to drop most their foliage and sulk. Keep it on the drier side and hopefully your winter cold is of relatively short duration. Don't bother feeding until it warms up again, and avoid shocking any remaining foliage by reacclimating to outdoor sun slowly, or you'll burn the foliage. Bougainvillea isn't the easiest plant to move back and forth inside and out, but it can be done If it's too big, do light pruning for size when you bring it in.

I live in New York where winters are never mild by a bougainvilleas standards, but summers are more than hot enough to keep them blooming well.
I have mine in a large 15 gallon pot and I bring it inside to a sunny window for the winter. It drops most of its leaves there and goes into a semi dormancy, but it usually manages to make a few blooms indoors which is nice to see in the dead of winter. Its not much of a problem indoors and I soak it about once a month and occasionally spray for spider mites. You might want to bring it outside on rainy or warm winter days and clean it off with a hose to get rid of bugs and to give it a bit of fresh and moist air.
They only need to go inside when temperatures get below 40F at night, so if you live in an area with warm winter days (55F +), you can take it out during the day and bring it inside during colder nights.
Bougainvilleas usually die when a freeze occurs, but if its comfortable and sunny outside during the day, and mildish at night, they will do great.
Good luck!
-Alex

You can overwinter Bougainvillea indoors quite easily. The only limiting factors are space - it is not a small plant -and sunlight. They need plenty of light throughout the year.One option in cold climates is to prune it back very ruthlessly in spring and grow it as a semi-bonsai. It still needs a lot of light, however, as it will flower in fall/winter.

I grew Bougainvillea for the first time last year. A Barbara Karst and a Helen Johnson over-wintered in the unheated garage without any problems. The BK even bloomed in late Feb in the garage. It got down to 8F this past winter here. My garage door faces west and I do have a fridge in the garage. This plus the 2 vehicles probably helped a little. These were both 3gal plants.

I also grew some small BK plants and a Vera Purple near a sunny south facing window inside. Some of them bloomed but the bloom color was very different.

I think they are pretty tough plants. I am careful not to overwater them.

I have had 2 large bouganvillas on trellises, in large pots for the last 15 years & a few plants in hanging baskets. I live south of Houston and they pretty much stay outside until we get a hard freeze warning. At that time, all we do is use a dolly & roll them to a spot under our covered patio & throw a couple of old sheets on them--unless we hear there will be very cold temps. for a few nights. . It usually warms up during the day & the sheets come off. They go semi-dormant during the winter, but come early spring (February 14th) we roll them back to their full sun spots, give them a good haircut, water, and they come back to life! Remember---they bloom on new growth so a heavy trim is a good thing!!! Good Luck!!!!!

Thanks for all the good advice! I feel more hopeful for a good winter over for my plants.