Be careful that you don't build a way for cold air to get to the bottom of the hydrant. If you have enough of a slope that the drain trench opens to the surface, that is awesome, but fill it with gravel to insulate. If your drain trench doesn't open to the surface, then aren't you just building a bigger pit?

If you keep the top of the drain trench close to the surface of the ground, and cover it with a thin surface of soil (with grass), then you have the very same thing as a septic system drain field - which as I mentioned earlier is really an evaporation field.

The water has to go somewhere. In dense clay it won't likely go downward - that is why you're having the problem now. It either has to flow elsewhere or it has to evaporate.