I'd be more concerned about the bilge pump function at this point. Considering the pump is in the lowest part of the bilge......which is where the water would have been which phase changed to ice......did the bilge pump freeze, or did the float switch freeze?
In either case, and especially if the boat is kept in the water, imagine what would occur if a big leak developed. Regardless, a bilge heater would remedy the problem, and avert any future issue of the same kind. Once resolved though, I would definitely check my bilge pump(s) and float switch to insure there is not a problem with the function of the system. A pump or switch which froze underwater could have been damaged, and you would not know until you needed them and they let you down.
My two cents.
V1