During the winter months the soil becomes colder and the grass cannot grow as good or at all in the cold soil and also the sun is not shining as much in the winter either.
The grass needs good warm soil as well as plenty of sunlight to properly grow and thrive and it also needs water if you want the grass to stay green.
Most often in the winter you'll notice lawns sometimes become dead looking and brown but then the grass returns to green and starts growing again when the spring weather comes and the soil becomes warmer again.
The grass needs warm weather, warm soil and sunlight to properly grow so it's natural for grass to go dormant or grow slower in the winter months.