Staining
Hey, Pat! Your staining will go fine as long as the wood is completely dry (12% moisture is the target.) If you don't have a moisture meter, but the wood has been cleaned and sitting dry for a good while, you are probably OK. This time of year and at the temps you and I are living with this week, I would want the fence to sit dry for a week.
There are no temperature limitations on RS. If you were using a product that had any coating properties, you would see words on the container like "Do not apply if you expect the temperature to drop below 54 degrees over the next 24 hours." I used a product once that had that warning in spite of some very cool temperatures, and the stuff turned white overnight. It all had to be stripped and replaced, on my nickel. Oops!
One more idea - electric socks. I can't believe we dipped down into the 20s in Hotlanta.