It really depends on the hores fitness and the pace you are doing. If you are just walking horses can travel REALLY long distances but if you are trotting etc then a fit horse can travel up to 160km in 24hrs. (this is with breaks every 30-40km.)
Are you planning to ride long distance or something? The best way to make sure your horse can handle it is to train them according to the distance you want to ride.
If you want to do a long distance ride whether it is competitive or just for fun let me know and I can send you some info on preparing a horse for long distance riding.