I don't know about any dog restrictions, but about 20 miles outside of Helena there is a campground at Canyon Ferry Dam and reservoir. I haven't been there since the CG was built, but I lived (during my 'teens) in the construction camp during the construction of the "new" Canyon Ferry" dam. (There was an original Canyon Ferry Dam which was inundated when the new one was built.)
You can probably get some information from the U.S. Bureau of Reclamation, as they (we) built the new dam, and still operate it. I don't know what agency (local state or federal) is operating the CG.
The dam is located on the Missouri river.