On a steep downgrade, the issue that would concern me the most is the possibility of overheating the brakes. Overheated brake rotors can warp, and overheated brake fluid can boil (literally!)–resulting in loss of braking ability–if moisture condensation has diluted the brake fluid.
If your brakes are getting “soft” on downgrades, this indicates that they are heating up too much, and this is potentially very dangerous. If this has happened on your car, and if you have not had the brake fluid changed in the past 3 years, you need to have your mechanic change the brake fluid.
So–if you are driving on a long steep downgrade, such as described, I would suggest shifting to a LOWER gear (your terminology is skewed), and also using the brakes to control the speed of the car. Don’t worry about the engine or the A/C, as they are not affected by downshifting to a lower gear.
Of course, if you decide to downshift to too low a gear, then your engine will be turning at much higher RPMs, so the idea is to downshift one gear at a time in order to find the correct lower gear. If your transmission is a 5-speed, shifting to 4th will not be adequate on a steep downgrade, and a downshift to 3rd is probably necessary. Downshifting to 2nd would be too extreme unless you are driving at…let’s say…less than 30 mph.
For those who believe that using engine braking on a steep downgrade is damaging to a transmission, I can tell you that I have used a combination of downshifting and braking on steep downgrades for the past 46 years on a wide variety of vehicles–both foreign and domestic–and I have never had a transmission problem. Zero, zilch, nada. Of course, I do change the fluid and filter every 3 yrs/30k miles, so that is a part of my flawless record with automatic transmissions.
If this practice was damaging to transmissions, don’t you think that I would have had at least 1 or 2 transmission failures in 46 years?