On second and third thought, you could pit compost the manure if you have a place you could put one or two manure pits.
If you have really well composted horse manure it's usually no trouble getting a gardener or nursery to haul it away.
I live in Virginia, and we frequently get temps of over 100 degrees for days on end in the summer, and horse flies that have to file a flight plan with the local radar tower. I can't imagine living on 2 acres with an open manure pile here, but I suspect with a different climate, it might be managable.
You might also consider doing the feed through fly control for the summer, or ordering the fly predators.