I'd turn on the propane, but definitely not the electric on the water heater. You can control the flame, turning it on a few moments and then turning it off. Although, it probably would not hurt anything to just flip on the gas and let it go.
That' what I'd do. Be prepared for a leak though. Hopefully, you had a large enough air pocket at the top of the tank for ice expansion and nothing was hurt.
Attempting to melt the ice from the outside of the water heater by applying heat will not be very effective. As state above, the heater is insulated too well.