Cold or Not......Ventilate the place until you can dry it out.......You've got at least two sources of the water..........the cars and the fresh concrete.........Any additional ground water source intrusion from the outside?
Let the concrete dry before you get carried away with the drywall.........
Poconos?...........is that 300 days of snow a year?
AFTER it drys.....How about an epoxy finish that would prevent the surface/snow water from being absorbed.........Is there any run-off pitch to the floor????.........The epoxy I used had a non-skid Floor surface with "walnut" shells added (from the manufacturer).........and it was applied up the walls and in the "corners" to provide complete control of chemicals in the shop............So it could keep the water out of the walls/floor but the snow water would still need to be removed (swept/vaccuumed/pitched) from the garage.....
.....Damn, a floor drain would be nice............Oh and maybe some radiant heat in that slab................