If the truck came with air conditioning, there will be a condensate drain tube on the passenger side of the firewall, under the hood. It will have about a four-inch-long rubber hose with a 90-degree bend in it hanging down. If water is dripping from that hose, the heater core is indeed leaking. This is common on GM vehicles, as is a leaking radiator. The biggest contributor to the corrosion is following GM's recommendation to replace the coolant every three years instead of every two years. They originally advertised it as "lifetime" coolant which led a lot of people to have leaks due to corrosion. The problem is the water pump lubricant, corrosion inhibitors, and other additives wear out in about two years, then the acids that normally build up in the coolant attack the metal parts.
The heater core is a good suspect for the wet floor and fogging windshield, but if the water is running out real fast, also consider corroded core plugs in the engine. There's usually two or three on each side of the block, and there's one or two on the back. The transmission has to be removed to replace those two.
There's some relevant articles here:
related to cooling system leaks, but at this point you already know what to look for.
Thursday, January 30th, 2020 AT 3:53 PM