This would probably work great for what I call "filth flies" (the same one that the fly parasites do a great job on) but horse flies tend to be "sight feeders" (i.e., look for movement), so this probably wouldn't do well with horse or deer flies.
I have seen people take small dark blue or black buckets (or even large plastic blue cups), drill a hole in the bottom just large enough for a rope, pass the rope through the hole with a knot in the end so the rope can't go all the way through the bucket, and hang the bucket after covering the outside with something sticky (can be corn syrup/water boiled, petroleum jelly mixed with various types of things, Tangle-Trap Sticky Coating, Tanglefoot Tree Insect Barrier, or regular fly paper using double side tape).
The idea is when these are hung, they can sway in the breeze (so should be placed outside)... when the horse fly lands, it gets stuck. If you use large plastic Solo cups (blue) you can just throw them away when they are full. I saw one person buy a hard hat from Home Depot, paint it blue, cover it with plastic wrap, and then paint it with Tangle-Trap and then set it out... when full, strip off the used plastic wrap, put more on, repaint, repeat. I have a bunch of black pots that my flowers came in this spring that would work great.
This person just puts the cup on a post; I find it works better if they move. How to Make the Ultimate DIY Deer Fly Catcher - Quarto Homes