Does it stink like anti-freeze?  Is it dripping out of the floor vents?
When you run the defroster, do you see a mist coming from the vents?

If no to all three, it's not the heater core.  If it only gets wet when you
run the A/C or the defroster, then I'd suspect a plugged evaporator drain.
If it only gets wet when it rains, I'd first suspect a leaky third brake
light gasket, then I'd suspect a leaking rear window seal, then I'd suspect
a bad door seal.