Welcome - cold enough for you?
How old are your batteries?
Do you have a multimeter? If so, when the truck is warm (meaning after the grid heaters have cycling), check the voltage at the battery terminals to see what the alternator is putting out. It should be around 14V or so - any lower and the alternator may be the culprit. You could just have a bad ground - you could remove and clean all grounds. At the very least check the grounds and make sure they are tight. Also, check the connections at the grid heater plate.
If the batteries are more than a few years old, I think Id take them to partsource or Canadian tire and have a load test done. Also, if needed, they can test your alternator as well. I think at minimum, you are going to need to change the batteries.
I replaced my batteries this fall and I had some of the same oxidation that you are describing. I switched to Optima red tops (Group 34/78) and because these batteries are AGM material, they dont corrode and you never have to clean the posts or clamps.
Again, welcome to the site
One last thing - dont ever use a rubber tie down or bungee strap on a battery