Horse sperging ahead:
If you are writing a medival fantasy (or any kind of fantasy where horses are a main source of transportation) then please, for the love of all that is holy, do some research into horse breeds.
More specifically, if you are writing an adventure story where the protagonist has a horse then make sure you aren't giving them a steed which would probably die within the first day of any long distance travelling.
Friesians are the worst offenders for this. While yes, they are the closest relative of the destrier horse, they still would be a terrible choice for a long journey because they aren't built for it. Destrier horses were only accessible to nobles and wealthy knights who really only used them for show just because of how expensive they were even back then. I have lost count as to how often I see characters on TV use friesians for the wrong purpose in fantasy/historical fiction- nobody would want to risk losing such an expensive horse back then! (Looking at you, George RR Martin!)
A rouncey horse would be much better suited for such as a task because they were mass bred, cheap and therefore disposable if they died on the journey. Sure, they're usually not as majestic looking as your destrier or palfrey, but they're practical! Also, if your story takes place in the winter then the horse is going to have a nice, fuzzy coat- again, not as majestic as the Hollywood horse, but it would add a layer of realism to your works.
While we're on the subject of horses: stallions.
Writers love stallions. Hollywood loves stallions. Even the word stallion has a more romantic flare than gelding or mare does.
However stallions tend to be a lot more unpredictable than geldings or mares are. They have testosterone driven aggression and are in general more difficult to handle. Sure, some stallions are perfectly well behaved but they're far and few in between. There's a reason why it's preferable to have them gelded at a young age, after all.
Unless your character is established early on as an experienced horseman, it would be wiser to give them a mare or gelding for their journey. Even in the Middle Ages, most people usually didn't use stallions very much outside of show and breeding.
Sorry for the rant- having grown up with horses, things like this just bug the crap out of me.