Your wood look like teak
If schedule-wise it works better for you to strip it now, go for it. Teak
is just about the most dimensionally stable wood there is and shouldn't move around too much bare. Your finish is shot anyway.
Also, I see no reason you can't get a couple of thin sealer/build-up coats on between the rains. If it's more than 50 degrees for a few hours and dry for more than six (just making up numbers really, this isn't laboratory science) it'll cure eventually.
If you're going to varnish
in cold weather
, I'd also recommend Epifanes. In my experience, best varnish
with in cold weather. Never had a problem with cure. You'll probably need to pre-heat it to help flow.
Advice is worth what you paid for it.