You can wake it up, but don't expect it to be happy. How much do you like being woken up in the middle of a sound sleep to cold, unfriendly weather and inadequate food? (And by food I mean sunlight, not bugs.) Don't be surprised if the plant dies next year.
If you do wake one up, give it plenty of light and gradually warmer temperatures, to keep your plant energized and make sure it thinks that it's springtime. And keep an eye on it later in the season, as it will probably tire faster than your other plants and require an early dormancy next year. Also, treating with a little Superthrive might help.
Best luck,
~Joe
PS - Your plant will be weakened by coming out of dormancy early - I wouldn't count on it surviving being cut in half under those conditions. If it's for some project, I'd go get a hardware store rescue trap, nurse it back to health for a few weeks, and show that. Whatever you find in the store this time of year will already be out of sync for this year's dormancy, so it shouldn't matter.