Yeah, it definitely sounds like a dog and dog owner problem. Hard to get a horse used to dogs when they really are threatening or underfoot!
I used to be able to bring my old Aussie to the barn. My old horse was pretty sensible about dogs and the dog was not allowed to go in the field or to “play” with the horses. I would tie him by the side of the ring when I rode so the horse was used to him. Then, when I was riding alone, I would let the dog loose to follow us around the ring. Horse was fine with that, so eventually we headed out on the on-property trail. At first I would call to the dog and keep him where I could see him. He enjoyed crashing around in the brush, and since the horse knew what it was, it didn’t really startle him. Finally I could let the dog go wherever and the horse was totally fine with the dog running from any direction (we could always hear him!) Now silent attack deer on the trail were no longer a problem! :winkgrin: Never brought the dog on trail when riding with someone else.
OTOH neighbor had an obnoxious setter that would try to chase the horses. He tried chasing us in the ring.(This was after Aussie was gone) My horse wasn’t really scared, but the dog was persistent and when we tried to chase it, it could circle around faster than we could and kept nipping at his heels! I got off when the dog grabbed his tail. Wish the horse would have kicked the dog just hard enough to send him away, but he didn’t. I had to actually throw rocks and hit the dog to get him to back off at all.