I just want to point out that many people are talking about if you could or not shoot someone dead-If someone attacks you you don't have to shoot them in the head. You could probably shoot them in the knee or something. I'm not actually a gun-person but that was just my first thought whilst reading these posts.
Here in NZ we are not allowed to carry guns on public beaches but many people ride on the coasts. As NZ has many beaches they are not crowded (often deserted) so it is totally possible someone could be attacked whilst riding on the beach. I know on rider with a good self defense plan, they have a large machete (sharp) strapped across their horses shoulders. If complained at they say it is for the cutting away of gorse when they ride over the dunes, but its most important purpose is to serve as a very visible detour to anyone wishing them harm.
This idea could be adapted for riding in pretty-much any wilderness area.