I would leave them out too. Especially since they have shelter there that they can use if they want. Once you get your barn wired I would definitely put some fans out, it helps a lot for both the horses and you. Also, if your horses are sweating a lot I would suggest hosing them off, it'll help to cool them down for a little while. Another thing is to use lots of fly spray and even a fly sheet (they even make some that reflect the sun too to keep your horse cooler) to keep the bugs away because if they're not stomping or running around trying to keep the bugs off they'll stay much cooler.