Orienteering is a sport in which you have to cross unknown territory with only a map and a compass. So, of course, some people do it on horseback. (The rules are slightly different, but basically you have to get from point A to point B whilst passing through several intermediary points).
It's somewhat popular in America but unusual in Europe these days (probably because of lack of space). Like many equestrian sports, it grew out of skills useful to a cavalry officer.