It's common knowledge that trees become bare during winter, but not many people actually know how they keep themselves alive during the bitter cold. The animals you see during the winter keep moving and eat more food than usual to survive winter, and the ones you don't see are hibernating. Trees go through a process similar to hibernation called dormancy, and that is what keeps them alive during the winter.
Dormancy is like hibernation in that everything within the plant slows down. Metabolism, energy consumption, growth and so on. The first part of dormancy is when trees lose their leaves. They don't make food in the winter, so they have no use for masses of leaves that would require energy to maintain. When it's time for trees to lose their leaves, a chemical called ABA (Abscisic acid) is produced in terminal buds (the part at the tip of the stem that connects to the leaf). The terminal bud is where the leaf breaks off when it falls, so when ABA gathers there, it signals the leaf to break off. (This occurs only in deciduous trees — not in coniferous trees.)
ABA is a chemical that also suspends growth, preventing cells from dividing. This is something that occurs in both deciduous and coniferous trees. Impeded growth is another aspect of dormancy. It saves a lot of energy to stall growth during the winter, and during the winter, the tree isn't making any new food for energy. It's similar to hibernation, since most animals who hibernate store food as fat, and then use it to run their essential systems during the winter, rather than grow any more. The tree's metabolism also slows down during dormancy, and this is part of why cell growth is impeded. Since it has to conserve the food it has stored, it's best if the tree uses it up slowly and only for essential functions.
It is possible to force a tree to evade dormancy if you keep it inside and with a stable temperature and light pattern. However, this is usually bad for the tree. It's natural for trees to go through dormancy cycles, and the lifespan of the plant is dramatically increased if the tree is not allowed to go dormant for a few months. Trees have winter dormancy for a reason, and it's best to just let them run their course as nature intended.