Depending on what you mean by "cold" and "dry". Statistically, the states with 1-2 days of rain (greater than 1/4") in October and November rain are AZ, CA, & NM. However, the November 1st average high temps are typically in the low 70s in AZ & Southern CA and the mid-60s in NM with lows in all areas getting into the 30s by mid-November in all areas. Personally, I will do 30 degrees if I hate to but do not go looking for it.
If you have not done so, you could always do the ST. If it gets too cool in NM, dip south toward the border where it warms up ~5 degrees warmer. The Portal, AZ area is quite nice. Keep going and soon you will be in the Gulf Coast region with temps in the upper 60s to low 70s until Florida where you can dip south to Key West and sip margaritas until you have to go home. Note that you will have 5-6 days of rain per month east of central Texas.
If you are willing to do Mexico, do CA, AZ and circle back through Mexico.
Have a great ride!