There is a lot of information here on overwintering. (I don't have to do it, I live in So. Calif., so can't give specific advice about it) Search the forum for 'overwintering'. You will probably want to bring the boxwood into an unheated garage or something. But the house, in the winter, is too dry usually. The boxwood would do better outside. It may look like a delicate little tree, but you'll hurt its feelings assuming that it needs over protection. It is, after all, a tough and venerable bush.
Let us know how it goes. Keep it damp but not wet. You may see new growth up close to the trunk... that will be a good sign. If so, keep an eye out for aphids. If you see them, remove them with a Q tip and squish them. Your tree is in a vulnerable position, and can't take much messing with.
edit: you can remove the green moss, but it actually won't hurt to have some on the tree or the soil. In your damp climate, it's probably pretty hard to escape moss. Remove it carefully, if you like, but unless it is harboring bugs or is keeping the water from soaking down into the soil it really won't hurt the tree.
Joanie