Surprising though it may seem, I have read that horses and cyclists (and, I assume, pedestrians) are the only 'traffic' using the roads 'by right'. Everything else has to be licensed...
I'd suggest that the chance of a random dog eating a random bit of horse dung and getting ivermectin poisoning is so low as to be almost invisible. It's mostly likely to happen to dogs that are around horses a great deal (like, most horse owners seem to have dogs which go everywhere they and the horse goes). And horses aren't continually fed with wormer - they're probably. wormed 2 or three times a year. I've no idea how long the ivermectin remains potent.
And, if you can't see a steaming great pile of horse droppings and avoid standing in it....
If you do manage to tread in some, they don't have the same adhesive quality as dog or cow poo...