There are a number of reasons why the leaves turn brown in winter.

The earth further away from the sun in winter, the earth spins in a egg shape, the bottom of the egg is nearest to the sun which is summer. For plants to make food it has to go through a process called photosynthesis. Photo means light and synthesis means energy. The plants absorb light using their leaves, because the sun is far away there are less light beams for the leaves to absorb. Light on its own cannot make the plant grow it also needs water which only can be absorbed by the roots underfround.

What happens to the water?

Because the sun is further away, not enough heat is distrubuted into the earth, so all the water gets frozen and cannot be sucked in by the roots.