Assuming your heroes have a horse each, how far can they travel in a day without damaging the horses?
The American Endurance Ride Conference allows 12 hours to complete a 50 mile ride, and 24 hours for 100 miles. However, these horses are not covering this distance for days on end. They're rested after the race. It also can take several years to properly train and condition horses for 100 mile races.
A more reasonable figure, thus, would be about 30 miles a day - assuming a fit horse on reasonably level ground. In mountains, you might be doing well to cover 15 miles in a day. And this is staying in the saddle all day, which might not be feasible in any given situation.
Obviously, if your characters only have to cover 100 miles or less and are in a hurry, you could assume they could do it in less than 24 hours. The horses would need to be rested afterwards (and so would the riders, trust me), but it could be done safely for the horse.
For a normal, leisurely trip, such as the Starks going from Winterfell to King's Landing, I would generally apply a ballpark figure of about 20 miles a day.
On the other extreme, post riders can get a message from one end of a continent to another very quickly. The Roman post rider system averaged 50 miles a day and the famed Pony Express hit 75 miles a day. How? By using a relay system. The rider would change horses at regular intervals. Over longer distances, post riders would cover a specific shorter route and hand off letters to a different rider.
Hopefully, this gives some idea of reasonable travel times. (Obviously, if your characters are in dire straits and don't care about ruining a good horse...)
A good horse after a long day's work. (I know, I know, I keep showing this girl, but she really is a very nice horse).