If the player party has some people with access to horses and others not, it means they can't ride on roads to save time on journey? Or some arrive later? Or they're split as different parties for the journey part making separate rolls altogether?
The company will still almost always travel together, barring odd circumstances: having to split to achieve two goals or maybe one of you needs to race ahead on horseback to get a hobbit back to Rivendell to heal a morgue knife wound while the others travel on foot, as far fetched as that sounds.
Otherwise you’d need to all split in to mini companies with their owns guides, scout, lookout and hunters. This is dangerous and slow (few characters can cover such a range of skills). Even more dangerous if is small group runs in to adversaries.
Those with horses will still enjoy the fatigue reduction, and the company can still travel on roads to get 1D bonus on events. But they won’t benefit from the “all mounted” speed bonus.