My 02GT had a major water leak on the right side. Turns out there was a 12 inch gap
with no sealent on the right side of the windshield. Some one / thing goofed!
this is sort of common on many late model fords. the cowl weatherstriping gives and then you end up with a puddle on the passenger side floor. if it gets deep enough it can flood the rear too. happens mostly on focus and taurus but it's possible for it to happen to a mustang too.
I highly doubt it's your heater core. Plus if your heater core was leaking bad enough to flood the floorpan you would have major overheating problems. One last thing on that I think you would notice if the puddle was green.