I may be wrong but i didnt think dogs were allowed to be off the lead when on a bridle path? and i certainly think a dog that cannot be controlled by its owner should be allowed on one. 
Ill tell you for why.
I went out with the RS on a hack yesterday, we went along a bridlepath and there was a woman with a bull mastiff x and some small rat like creature, which were not on leads but she held onto them as we passed. we all said thank you and carried on, we a had a little trot and about 5mins later this mastiff appeared from behind out of nowhere and barked and tried to bite the ankles of horse at the back. this then made 8 horses (including the RIs) all bolt forwards along a narrow path with a steep drop on one side untill we could get them under control. The dog ran off and the owner was nowhere to be seen.
We had already had a near miss earlier in the ride when one of the horses went down this steep bank in canter and when it came back up sent my horse into a few strides of gallop. but it certainly wasnt a boring ride
Ill tell you for why.
I went out with the RS on a hack yesterday, we went along a bridlepath and there was a woman with a bull mastiff x and some small rat like creature, which were not on leads but she held onto them as we passed. we all said thank you and carried on, we a had a little trot and about 5mins later this mastiff appeared from behind out of nowhere and barked and tried to bite the ankles of horse at the back. this then made 8 horses (including the RIs) all bolt forwards along a narrow path with a steep drop on one side untill we could get them under control. The dog ran off and the owner was nowhere to be seen.
We had already had a near miss earlier in the ride when one of the horses went down this steep bank in canter and when it came back up sent my horse into a few strides of gallop. but it certainly wasnt a boring ride