So how far can a horse go in a full day? It depends on the horse, but generally speaking, 30 to 40 miles. Cavalry marches were typically 30 miles or 40 miles in a day, covered over a period of 10 hours. The distance can be covered either by traveling 10 miles at a time at a high speed, followed by long intervals of full rest, or the horses can be on the move through much of the day but at slower speeds, with the riders dismounting sometimes to walk beside their horses.
Horses in the wild naturally travel about 25 miles per day just grazing and moving about their territory, so 30-40 miles is not that big a stretch for them, provided they are well managed and in good condition.
Some horses, bred and conditioned for endurance, can go much farther. Arabian horses are known for their endurance, and competitive endurance horses (mostly Arabians) can go 100 miles in a day. That’s exceptional, however, and it would stretch plausibility if an ordinary horse in a fantasy novel, without special conditioning, traveled that kind of distance on a regular basis, especially if it were a big warhorse. You’ve seen Olympic-caliber marathon runners, and they’re not big and burly. Same goes with endurance horses. They’re small, sturdy, and fine-boned.