I had precisely the same concerns about my shop temp (between 40 and 50 F) last year when I was building my Great Auk. The glue never failed and the boat turned out fine.

I actually tested the glue at varying temperatures. I glued two strips together at 75 F and two more at 45 F. When they dried I tried to break the strips at the joint. I had the same result with both pairs - the wood broke before the glue. You might want to try the same type of test at the temperature you are working in.