I have 2 dogs that are not used to horses and that walk on a lead on roads and run free in fields and parks. Whenever we see riders, my little dog will yelp and bark like someone is murdering her and hide behind me and my big dog will just continue doing his sniffing thing in the brush not bothered at all.
The problem is, this little yappy dog could be taken as aggressive when in reality she is terrified.. Would you shoot or mace her because she was scaring your horse?
Don't go 'guns blazing' hurting a possibly nervous or scared animal because you or your horse feels threatened. See if you can deal with it in a less violent way first..
OP - in your situation, I would have gone guns blazing. Great Danes are meant to be big docile beautiful dogs, whoever owns them should be shot!
Before anyone questions my dogs behavioural issues, I promise we have tried almost everything and when I return from Oz I am getting a 'dog whisperer' to see if that will help.. she is nervous and scared all the time and we don't know why and have tried everything to fix it.