If it's like the Portland area (where I am) I wouldn't worry about it- it's not all that hot or humid here. You might talk with your BO to establish under what weather conditions you want your horse kept inside (i.e. During the hottest part of the day when 90' or higher) and ask if they'd be willing to build a run-in or other shelter in the pasture.
For the flies, fly spray and a long fly mask would be improvements. You can even spray the fly mask with fly spray (let it dry before putting it on the horse, though). If your horse's face is dark, then a light colored fly mask might actually be cooler for her (same with a light colored fly sheet).