Why Is It In The Winter Months That Trees Lose All Of Their Leaves?

The trees are designed by nature to cope with all kinds of weather and don't feel the cold in the way people do.
Thousands of years of evloution means that the trees have evolved to cope with the cold weather. It's natures way of coping and ensuring that the trees survive and will come into their own again in the spring time.

Not all trees do lose their leaves during winter only deciduous trees. The reason these trees lose their leaves has to do with a chemical imbalance. When it becomes cooler out the leaves can't produce a certain chemical they have to keep them connected to the rest of the tree resulting in the leaves falling off.
There are other types of trees with varying lengths of time they lose their foliage.