welcome to the forum! there is no species called a "eastern box tortoise" but there is a species call an eastern box turtle. what the cold side and basking spot temps? are you using a coil bulb? reptiles need heat to function, so i don't think she "likes the cold" i guessing its something to do with the heat or lighting. like said above pictures of the tort and enclosure will be extremely helpful.
If your box turtle stays on the cooler side of its habitat, maybe you should place another heat source/light over the cooler side. You DO have the turtle set up in a regular habitat, don't you? and not running loose in your room? Turtles need their own space where the 'weather' is regulated, with lots of dirt to dig into, some plants to hide in and plenty of food to eat. If you want your turtle to grow big and strong, give her a nice, warm habitat to call her own.
Are you saying that your tortoise is on the loose in the house?
Provide a proper habitat and box the poor thing in, in as big a space as you can manage. Otherwise the humidity & temps aren't right, the light & uvb aren't adequate, and it's probably trying to hibernate. That's not safe.
You didn't mention where you are or what kind of tortoise.