In the past three weeks, we've received the equivalent of three inches of rain, so the frozen soil is holding a great deal of moisture. The trouble can occur as things begin to warm up, since the first area to thaw out is at the surface. With frozen ground below, the water near the surface can't percolate into the frozen ground beneath. As seen in the picture, as the snow melts, water often just runs across the surface.
What happens if golf carts are allowed on these areas too soon? The turf may experience shearing of the roots from mechanical injury, as if a sod cutter had been used on it.
So please understand that if carts aren't permitted at times during the winter, we're not trying to be Grinch-like. To the contrary--we're protecting the course for the long run, so you will have the in-season conditions you want.