That's about the temp here too......FINALLY. We have had all that below and wind chills etc. I never glue in those temps. Must be up in the 50's. The only finish I would apply in those temps is a wipe on poly. Should be fine. Staining, shouldn't be any problem either. I would stain it and then bring it inside so it can dry properly. Actually if you can put wipe on poly and then bring it inside... all the better as well. Any spray on finishes like lacquer and other varnishes I avoid. And of course, there's always sanding it well and just using a paste wax.
You say avoiding poly, do you mean because of sagging and hard to apply because of all the different levels and in between areas etc.? If so that is wear a wiping poly will help. I make my own with equal parts Minwax Oil Gloss Poly, Mineral Spirits, and either pure Tung Oil or Boiled Linseed Oil. Hope this helps!
Corey