Taz, don't do it. It'll be scabby in no time at all. Also, paint has difficulty adhering to zinc. There will be patches where the water will get through the paint, either because of bad adhesion or just wee bits of the inevitable damage. These bits will be sacraficial just like your engine anodes and the area will bubble up. The whole point of the galvanising is that it is sacraficial and it deteriorates gently. When you paint it, because there is limited access in these areas of damage the zinc gives itself up vigorously.
Been there, done it and certainly wouldn't do it again.
Edit: I see silversurfer appears to have had success. Your call.