Living in SoCal Desert, not far from a couple of the big aircraft parks I can state that carbon steel does still rust though not as fast. Some of the big tanks and old corrugated buildings etc show considerable corrosion, though as suggested above if does appear to be mainly cosmetic.
Oh, and it's not arid all the time, for instance very wet last week. How much of the corrosion is tied to those occasional wetter periods I'm not sure.
the corrosion rate is a function of many factors
like presence of Atmospheric contaminants (SO2, HCl, organic acids), distance from the sea...but usually the corrosion rate in a arid desert is very low for carbon steel and weathering steel
this is from a paper of NPL:
“Weathering” or “slow-rusting” low-alloy steels containing 0.2-0.3% copper with minor additions of other elements corrode at about 3 1 to ¼ the rate of plain steels.
In the driest atmospheres, e.g.at Khartoum, the rate can be as low as 0.003 mm/year.
