Hi Lenny
With water in the REAR footwell it would seem unlikely that is the battery plenum. More likely to be the rear screen washer tube which runs underneath the carpet on the passenger side, next to the door sills. It could be that there is a join, or small hole in the pipe.
I understand that in cold weather, with not enough concentrate of screen washer in the system to prevent the water freezing, the pipe and contents freeze. When you operate the screen washer pressure in the pipe increases because of the frozen blockage, and something gives, dumping water all over the floor.
As others have said, the front foot well is worst, as the water penetrates the electronics and all the fun then starts.

Tazz