There's no problem with building in the cold. Glue takes longer to dry and you shouldn't paint until you can maintain a temperature of at least 70F.

No matter what the temp, everything should be acclimatized to your work environment. Don't bring a kit from a heated house into a non-climate controlled shop and start building immediately. Let it sit for a week or more. Otherwise, the wood will swell and shrink at different rates and you may end up with lots of bows and warps.

Same thing applies to bringing other wood into your shop like a stick from the hobby shop.

Somebody suggested taking the plane indoors to cover. I would do the same thing in that case. Give it several days to acclimatize before covering. Maybe not necessary at that point, but still a good idea.