I have a 1 1/2" water line ran underground from a spring(pump fed without power turned off in the winter) to my cabin. Unfortunately it has to cross a bridge(about 20') to get to the cabin. Under the bridge, we insulated the pipe and enclosed it in a 4" PVC pipe. Because we were not there for long periods last winter, the water froze up under the bridge. My question is; Can I put a heat tape with a thermostate around the 4" PVC and then put insulation over it. It would also be exposed to the elements such as rain,snow, and maybe overspray from the creek below. Would the heat tape be shorted by the weather?

You can use something equal to this:

Raychem - WinterGard Wet - Light Commercial / Residential Pipe Freeze Protection - Light Commercial / Residential Heat Tracing Applications - Tyco Thermal Controls

Any heat trace cable will need to be rated for wet locations.

I am not sure I understand this application. The 1 1/2" pipe in inside a 4" PVC pipe full of insulation. If you use heat tap then it goes around the 1 1/2" pipe, not the 4" pipe. Your insulation would try to keep the heat away from the 1 1/2" pipe. Why not also think of a drain cock at the lowest point of the run, drain the water when you are going to be gone in the winter. Electrical power is expensive, especially when used to make heat and more so in remote locations.