Here is my $0.02.....
I buy hydraulic/tranny oil by the 55 gallon drum. It is stored, in the "use" position (on its side) w/ the cap loose. It takes me about 3-4 years to use up 55 gallons (just the normal dips/leaks on the tractor hoses, filter changes- I have 4 tractors). I haven't had an issue w/ the oil and it's exposed to outside temps (from 90F+ in summer to 20F in winter).
As long as your oil is not white creamy, I wouldn't worry. Granted, I don't know if your tractor is a hydro stat tranny...those are picky. Mine are all gear tractors and I did have one get some water to make it white ish once. I eventually purged all the oil out about 1 month after discovery (we were in middle of harvest, no time to take tractor out of the line).