|Greenhead fly: used without permission from Yankee Mag|
A little while later I got to thinking that greenheads may be closer to horseflies see below so I looked for a suitable horse related word. Herd, haras, or stable didn't seem to work--although a variation of the second option, a Harass of Horseflies does have some promise. I however went to The Four Horsemen of the Apocalypse for what I needed. There are various interpretations but the one I chose is one of the names attributed to the first horseman on the white horse, which gives me: a Pestilence of Horseflies.
So I did a little reading and greenheads are, in fact, a type of horsefly. They populate salt marshes, just like the huge tract of land directly behind the house we're staying in, and they are looking for a blood meal so that they can continue to lay eggs (200 eggs or so at a time!) I say continue to lay eggs, because its just the females that bite, and they only bite after they lay their first batch of eggs. Prior to that: vegetarian. They feed on nectar, etc.
Two last points: the season is apparently mid-July to mid-August (bully for us) and, they prefer to tear you open so that the can lap up the freely flowing blood, rather than poke you like a mosquito. Their mouthparts are so delicate that you don't feel them rip open your skin until they vomit up some digestive juices and anticoagulant onto the wound, which your body recognizes as foreign, and reacts with pain. That's why you're already bleeding when you swat at them.
Edit: Just to be clear, I may not in fact have been the person that actually came up with each of these brilliant ideas, I assume that it was a group effort, for which I am simply taking the credit.
They say that history is made by the victors, but it may be that history is actually made by the people who write it down.