Given the time of year, are you sure that this is not a freezing weather leak?
In really cold weather, you will sometimes get a cold weather weeping from the shaft. The shaft shrinks because of the cold and it will weep a little. If this is the case, I would not replace the pump for that purpose.
If it is a larger leak and it is indeed coming from the water pump, you will, of course, have to replace the pump.