Weather will be a factor. As will health -- blisters, colds, etc. And you'll have to stop every so often to rest horses, feed/eat, pee, and sleep.

Edward John Eyre tried.
Sir John Forrest rried he was gone about 115 days, (he went half-way and turned back, so I reckon that would be a fair estimate.

But you're smart enough to shift things pertinent to your needs.

In the settlement days of the old west, a wagon train would average 15 to 16 miles a day--slow mainly because the favorite draft animal was oxen. Horses were faster but not as sturdy. Tortoise vs. the Hare.
A troop of foot soldiers could do 20 to 25.
Mounted Cavalry, like has been said before, 25 to 30.

But in desperate circumstances the limits can be pushed--at the expense of men and horses.

I've read of journeys in which horses were pushed to do 60 miles a day or more. But they're completely spent within a week or so. Good for nothing buy Coyote fodder. I've also heard of men dying from desperate hard rides on a horse. Same goes for men. You push them too hard they wear out. No one can run a marathon every day--they simply can't ingest enough calories to meet the needs of their bodies.

And as far as calculating distances--I'm not certain, but I could guess that you could reasonably add about 1/3 of the linear distance to compensate for the inevitable bends in the trail. It's 300 miles as the crow flies, but 400 by road.

For instance, if you're being reprovisioned and remounted every twenty or thirty miles, with good horses and lithe, experienced riders, you could be going a hundred miles or more every day long enough to cross a major continent (particularly if it was important enough to kill a few mounts doing it). Systems like that have existed since prehistory, by the way. But what if the terrain (or climate) isn't suitable for horses? What if there aren't reprovisioning points at optimal intervels? What if you have babies in tow? What about altitude?