Hounds get off on scent trails and leave you. They are a pain on the trail in my experience.
The best trail dog we had was a hound - of undetermined type but very houndy. We had her before we got horses (1974) and almost had to get rid of her because as soon as she spotted an opening door she was through it like a rocket & off hunting in the woods - almost got shot for running deer. But once we had the horses, if they were out & going for a ride, she wanted nothing more than to be with them. If we walked she would disappear into the woods as we went along the trail to check things out, but always
stayed close enough to know exactly where we were & what we were doing, and never got in trouble while riding. (Running with our GSD after escaping through a door, that was another story. But never with horses.)
We had one German shepherd who was also exceptional with the horses - and better about staying close - but 2 or 3 others who were useless (not interested, or would nip at them, or had health problems that precluded long rides). So I would say it's the dog at least as much as the breed.
As for hair, the German shepherds left clumps of hair that clumped into monster dust bunnies and blew into the corners & under things - the hound left short fine hairs everywhere
Peanuts when there was nothing going on (1978 pictures):
Peanuts when she sees things are getting moving:
And when I looked through my scanned horse pictures, I found another pair showing the same thing (horses standing - dog sleeping; horses moving - dog up & moving).