OK, I'm a former Zonie, and though I live in an area where it does rain, I avoid it like the plague. The only times I've ridden in the rain is when I got caught. Would not normally start a ride in the rain, unless it's just a drizzle.
That said, I spent at least 75% of my tour this summer riding in pouring, torrential rain. It sucked. I can't see, my clear glasses get totally fogged and beaded up with rain, and when I the them off, the rain hurts my eyes.
However, you can stay warm and dry if you have the right gear. At the temperatures you are expecting, hypothermia is a real concern. I know some people here don't wear anything special to ride in the rain, but I have been very close to hypothermia after riding in conditions like you describe, to the point, that when I got back to my car, I put the heat on, stripped, wrapped myself in a beach towel that was in the car, and shivered for the 9 mile trip back to my house.
I'd wear a light weight wool base layer, with a rain jacket that has pit zips, waterproof gloves of any kind, and wool socks. If you can, get a helmet cover! It will really make a difference. Also, some toe covers for your shoes.
Yeah, and afterwards, take the innersoles out of your shoes and stuff them with newspaper. I used that trick at least 4 days on my 6 day tour in August.
Be careful. People in AZ freak out when they drive in the rain, the roads get greasy, and there's crap in the shoulder. Allow plenty of time for braking and cornering.

