I deal with a bit of an opposite problem in that my leather
boots are exposed to salt and cold, but with a similar result to the drying and cracking you described. If you like the utility of leather gloves, however, you can invest some time and materials into their maintenance to keep them in good shape for much longer. (When I was a kid, I had a little shoe care business, so my thoughts here are based on handling roughly treated shoe leather, plus my own
experience with my shoes in a snow/slush winter climate)
First, some kind of absorbent liner would be helpful, something like a thin cotton liner glove. It will absorb some of the sweat from your hands and spare the leather that corrosion. You can wash them between uses. That will keep the leather from getting as much salt saturating it. Sweat is really hard on leather.
Next, a damp cloth wipe-down after use will keep dirt and other things from abrading the surface over time. This will help keep the exterior in shape. Then, be mindful of not storing them in too sunny a spot; for day to day, handing them inside a closet or on the back of a door will let them air out without sunburning. If you're not going to use them for a while, put them away in a drawer, not air tight, but just to slow down drying in the air.
Finally, an occasional thorough cleaning with saddle
soap and a good oiling will keep the leather supple and prevent drying and cracking as much. I'm used to shoe leather so I have used the tins of shoe oil that my dad always used but have heard of using olive oil, lecithin, etc. A saddle shop would be a good place to look for ideas of what to use since a saddle would likely undergo many of the conditions you are dealing with.
Side note: I am curious how your son maintains the humidity in his guitars in that climate. Winters here are rough on guitars and I'm always looking for good solutions.