So, we talked about safe distances of travel - but just how fast is a horse?
Here's a handy little table/list:
Walk - about 4 mph
Trot - 8.1 to 12 mph
Canter - 12 to 15 mph
Gallop 25 - 30 mph.
Over a sprint distance (a quarter of a mile or so) a horse has been known to reach over 50 miles per hour, but they can't keep it up. Harness racers can trot or pace at the same speed regular horses gallop.
One of the things you'll notice is the much greater variance at the higher gaits. All horses walk at close to the same pace, but at the faster paces speed is affected by conformation and breeding. A draft horse is never going to gallop as fast as a Thoroughbred. (Yes, draft horses are perfectly capable of galloping, they just aren't built to do it very well!).
For normal travel, riders and carriage drivers tend to alternate walk and trot, hitting an average speed of 6-7 mph.
In mountainous or rough terrain you will probably be traveling mostly at a walk. The same if leading pack horses.
The ambling gaits are about the same speed as a trot, but can be kept up for longer by both horse and rider. To give some idea, I've spent 5 hours at a walk on a normal horse and regretted it the next day. I spent 5 hours on an Icelandic, mostly at the tolt, and couldn't even physically tell I'd been on a horse at all...
Horses should not be asked to canter or gallop for extended periods of time. Post riders would alternate between trot and canter. (There's a reason we talk about "posting" the trot - I'll talk about that tomorrow).