I've seen the sheetmetal impeller of a cheap Oldsmobile pump shear off the shaft. Pump shaft turned, no coolant flow. Ever since then, I've liked cast impellers rather than stamped-sheetmetal. But there's a huge number of stamped impellers that work just fine, year after year.
Whine in the cold was more likely PS or transmission rather than cooling system. Maybe even fuel pump.
Yes, the radiator will often freeze first, then the engine overheats. I suppose a water pump could freeze, more likely if it's aluminum rather than cast iron. Whether the impeller would tear off the shaft, or the belt would break is a toss-up.
There are no "air bubbles/air lock" in a cooling system at water-pump level; unless the radiator is half-empty. Some cars have cooling systems that trap bubbles; and they generally have bleeder valves on the high spots. These trucks don't. Even on level ground, the rad cap is higher than the coolant passages.