I had a Chevy Blazer from that era and you are correct! If it were cold and snowy the 4wd would not engage. But it wasn't the transfer case that was the problem - it had a manual lever that worked just fine. Back then GM had a front axle disconnect that used a heating element to heat gas which would then move a sliding collar to engage the front axle. And of course, when it was cold the gas would not expand enough to engage the front axle.
My understanding is that you can still buy a basic Ford Superduty with a lever-activated transfer case.