Where did you look this up? I'd be interested to see some information on things like that.
I would say though that 20-30 miles for a horse on a good road does not sound much. Somewhere in my mind is the number that the average walking speed for a man is 3-4 miles per hour on even ground. This would mean that it is certainly possible for a person to cover the same distance that you suggest a horse can. I would just assume that a horse could travel further than a man.
Probably wrong though. As I say, I'd be interested to see some information on this.