Source: “Der Wanderreiter und sein Pferd” by Sadko G. Solinski; and courtesy of Firlefanz, who actually wrote this in reply to a question on the message board
Basically it depends on horse, rider and terrain. At any rate it is not possible to gallop long distances. Generally a mix of gaits is preferable, although a steady trot is the best way to eat up miles, if necessary. Unfortunately it is also the least enjoyable gait.
Gait most often used is the walk, which may seem surprising. All gaits are never ridden at full speed, so you’d see a comfortable fox trot or a gentle canter, rather than any running.
Walk: 5-6 km / hour
Trot: 10-12 km / hour
Canter: 20-24 km / hour
A typical 2-hour schedule according to my book:
40 min walk – 20 min trot – 20 min walk – 20 min trot – 10 min walk – 10 min break. (This will get you about 15 km in two hours.)
Note that with this schedule you’ll reach the 30 km daily distance in four hours, and 45 km in six hours. This would be the limit for the average horse. (In effect, that leaves your travelling heroes time for sword practice, reading, cleaning tack, foraging … )
The book also suggests having a whole day of rest every three to five days, so the horses can regain their strength.
Travel times (in regions with seasons):
Summer: sunrise until noon
Spring and fall: morning till noon and mid-afternoon till early evening
Winter: mid-morning till mid-afternoon
My handbook is in German, so I have km as unit.
Generally, for a ride of several days, and with the same horse, you can expect to get 30 – 40 km without straining the horse.
Very good horses can go 50 km per day, and exceptional ones can reach up to 70 km per day. However, for such a feat they need perfect training, food and conditions.
In addition, it’s good to remember that horses are rather inefficient eaters of grass and need long foraging times or good, additional grain fodder.