Ideal operating temps for modern Automatic Transmissions are from 170F - 225F.
I wouldn't worry about 220F for a short time, especially when climbing a steep grade where temps tend to rise when pulling hard.
One important step when towing is to change fluids more often. Every fluid, engine oil, Atf, Engine Coolant, and Power Steering fluid take a beating under the heat created by towing.
On my vehicle I change Oil every 5K and ATF/PS/Coolant every 50k. So far my 19 year old truck (2004 Titan) tows my 6,000 trailer up anything I've encountered in the West.