The Eastern Screech Owl is fairly common here in north Texas, and it "nests" throughout cooler weather - starting now. However, Screech Owls don't actually build nests. They simply find a safe place (unused birdhouse, old woodpecker hole, rotted-out tree trunk etc.) and lay eggs there. The criteria are that it be hidden (so the owls can sleep during the day), the entry is at least 3 inches in diameter and the eggs won't just roll away.
In extreme weather the smallish owls may seek shelter in such a place (called "roosting"). If so, they're inclined to lay eggs there too.