I have my first oiled wood paddle as of this season. I usually store my paddles hung vertically on a rack in the garage. I live in a part of NY state with a lot of freeze/thaw cycling over winter. We get DEEP freezes from time to time, but more often it’s below freezing at night, maybe above freezing during the day, especially with the garage having plenty of southern exposure. The paddles are reasonably dry (wiped with bilge sponge) when put away. I haven’t have any issues with my varnished paddles after ~5 yrs. There’s not really a downside to keeping it inside, other than that I don’t have a great place to mount another rack inside and don’t fancy unnecessary holes in drywall.
I think the answer is don’t worry about it, but is there a chance that freeze/thaw cycling is more likely to warp an oiled paddle, to the point that it’s worth keeping it inside over winter? I assume it’s better hung vertically on a rack in the unheated garage than leaning in a corner in the house?