Fantastic and historical fiction is full of journeys, quests, hot pursuits, and other assorted road trips — sometimes with magical assistance, and sometimes not.
It’s with the “not” that things can get difficult, because a lot of modern-day writers don’t have anything like a working knowledge of any kind of travel that doesn’t involve an internal combustion engine and a four-lane divided highway. Doing research can be tricky, too, because while modern-day horse people (and trail hikers and dogsled racers and people who raise and train yokes of oxen for fun) are almost always delighted to share their specialized knowledge, a lot of the time it can be like asking a NASCAR driver or a rally enthusiast, “How many days would it take me to drive from Podunk to Ashtabula?”
You’ll get an answer, all right, but it may well be so full of qualifying details that you can’t sort out the single thing you really need to know, or so far out there on the extreme performance end that an ordinary mortal wouldn’t have a chance of coming near it. These people are all highly-qualified experts driving perfectly-maintained, high-end machines, and all you really want to know is roughly how long it would take an ordinary Joe or Jane driving a plain vanilla sedan with an automatic transmission and 50,000 miles on the odometer.
(I don’t know for sure, but I suspect that once horses stopped being a means of transportation and became a hobby, the equine equivalent of the midrange family car with automatic transmission and cruise control started fading out of the picture.)
Nevertheless, you have to try. Criticism of fantasy, both from within and from without the genre, has already said a lot of true and cutting things about fantasy horses that are functionally indistinguishable from motorcycles; you don’t want to provide the critics with yet more ammunition.
For some help on that, you could do worse than to read this LiveJournal post, here — also the comments, which contain much additional useful information.