This is a very common problem with old mustangs. The cowl leaks, drips on the floor and the water rusts out the floor pans. Opening up the cowl and replacing the sheet metal is the right thing to do. This process has been documented in many magazines and is no easy task. There are a few quick fixes out there.
Cowl vent cover
cowl vent repair kit may work if it is not to rusted out
Good Luck,
Jon