bobframe

I'd suggest that you check with your vet before you tried to take a dog on a "run beside me" tour. I'd ask his/her opinion on whether your dog could handle it physically, what precautions to take, how much food/water would be needed and get some advice on dealing with health issues (dehydration, torn pads, patching a wound, etc.)

I used to field trial and train bird dogs (English Pointers & English Setters) from horseback and the dogs were superbly conditioned athletes. A one hour trial (nearly non-stop running) was a lot- though the National Championships were three hours. Still, these were highly conditioned dogs with a handler, scout and gallery on horseback to watch over them. We still managed to have dogs get lost and killed on the roads.

I would worry a lot about a dog getting into trouble on a public road. Maybe different on a "Rails-to-Trails" or bike path environment, but even that has public road crossings, other riders, other dogs, etc. I'd have trouble enjoying the scenery and the ride experience if I had a beloved pet along- wouldn't be able to take my eyes off him.

You know that the right breed could handle the physical challenge (See: Iditarod") so with the proper training, I'd say OK. But those dogs are highly trained, built to take the conditions and the course is in highly remote areas, free of traffic.

While the idea has some romantic merit, I think the risks and challenges would make me say "not such a good idea". But hey, I'm a professional worrier.