You'll probably love Oct in PD
We live in the San Diego area so we go to Palm Desert several times a year, including the really hot periods.
I think that you'll like the weather. Mid October can be warm but it is usually quite tolerable. It is usually pretty dry and that makes a lot of difference. Rarely they get a storm coming up from Mexico that brings humidity with it. But that is pretty unusual.
If you want to do physically active things, do them in the morning and late afternoon. Save the warmer parts of the day to soak in one of the many pools, or be in the shade.
We've been to Palm Desert when the temps were in the 108 range. Warm, but we still had fun.
BTW, on Thursday nights, there is a weekly street faire in Palm Springs that you might enjoy. Also, on Sat/Sun morning (before it gets too hot) there is a College of the Desert "swap meet" (actually a large number of vendors selling unique clothing, food, fruits, and jewelry) that you might enjoy.
Last week we were in Palm Desert and I did some strenuous hiking in the desert with 90 F weather. Very pleasant and not hot.
Most of the parking spots at the Marriott TS in Palm Desert have overhead shade structures to keep your car a bit cooler.