My '02 Ford F350 Crew Cab doesn't do that. Maybe the serpentine belt is slipping on the AC compressor's pulley making the high pitched whining you're describing?
When towing, the under hood temperature may be higher, aggravating a slipping belt situation. When it's hot outside, the under hood temps could also be higher and the compressor may be presenting a higher load on the belt due to it working harder.
These are just some guesses, but it's a place to start. Also, if not the belt, maybe the belt tension idler pulley has a bad bearing, could be a bearing in the water pump too.
If you post your question on the "The Diesel Stop"
forum, I'd wager you'd get a lot of feedback. Those guys live and breathe Fords.