But I would love to hear from people who have already ran it, just looking for the best way to handle it, both mounted and unmounted, unless I cheat it a bit and try and force the players to do it mounted, but that seems a bit rail roady. I'm probably just being an idiot and not thinking through it properly.
In my game it turned into something like a hybrid of both. They
were on horses when they left the city, but between the group's historian and the character who was a Gate Pass local, they identified the likely ambush site and paused before they got there. The sneaky character and the acrobatic monk climbed up the side of the canyon to scout, spotted the guys lurking up there with thunderstones and mauled them, and proceeded to use the stones to spook the Black Horses' mounts instead. The hunters realised the plan had gone wrong and tried to rush the group instead; meanwhile the paladin, the barbarian and the artificer charged in and immediately dismounted, since they consider horses a bit of an over-complication in combat (I have a very non-archetypical paladin

).
So yeah, ultimately they still fought the combat, but it was more about skill usage than combat powers. By the time Kathor got there it was all over bar the shouting; since there was no way the PCs
couldn't beat Kathor just by himself, I had him hesitate and call for Renard to give up, instead of joining in. Renard kept fighting anyway, mosty because I thought they'd rather finish beating up the jerk, but rage at Kathor calling his masterful plan a failure made a good enough excuse.
In the end it worked out fine, but it was a very different encounter to the unique chase scene that was supposed to be there. I let my guys off a bit easy by having the hunters charge in after the trap was ruined - if the hunters had still waited, they might have had to mount up again and proceed - but they had already invested a good amount of time and effort in getting around the trap, and I didn't want to punish them for that by drawing out the combat part as well.
If you
do want the chase - which in all fairness is very cool - I suggest you try to keep them mounted if you can. If they are allowed to start thinking about it as a tactical encounter, they probably will, and tactical-encounter-round-structure will probably just get in the way. If she's there, maybe have Torrent argue that they can't afford to slow down by going on foot? There is an army not too far behind them, after all.
(Of course, all this is said about my group, who have an entertainingly consistent aversion to horses. YMMV. I hear other peoples' parties actually acquire the beasts as permanent vehicles! My word I have never seen such a sight.)