Strangely I was doing a little research on how far a horse can realistically travel in one day and after much google-fu it seems to depend very much on the type of horse, conditioning (i.e. is it used for long distance travel all the time, rather than been standing in a field for months, or only used for racing, etc..) and condition (i.e. is it well fed and watered), as well as how heavy a load and the terrain involved.

..anyway this is the list of distances (in miles per day) I've come up with from a variety of sources that I shall be using personally:

On Roads / trails
Level or rolling terrain: 40
Hilly terrain: 30
Mountainous terrain: 20

Off-Road (or unkempt trails etc)
Level/rolling grasslands: 30
Hilly grasslands: 25
Level/rolling forest/thick scrub: 20
Very hilly forest/thick scrub: 15

Un-blazed Mountain passes: 10
Marshland: 10

An average quality horse, of a breed suitable for riding, conditioned for overland travel and in good condition.
Roads and trails are in good condition and up kept by whatever local authority deals with them.
Weather is good to fair, and travelers are riding for around ten hours a day.

Halve these distances for a horse pulling a cart or for a very heavily laden horse (e.g. a fully armoured knight who insists on wearing his armour all day rather than having it stowed on a second baggage horse as would be normal!).

Add half again for specially trained horses and riders who are prepared to push hard (rangers, scouts and messangers, etc...) though do bear in mind that horses cannot be pushed like this for more than a few days at a time. You can add a bit more again to this distance if the breed of horse is exceptionally suitable for this sort of thing, but I’d say 2 to 2.5 times the base is the absolute maximum without some sort of magical assistance!

Poor weather such as heavy rain or wind should reduce distances by about one quarter, and very poor conditions like heavy snow or gale force winds, etc.. should reduce distances by at least half if not more.

Finding a place to ford a small river or swimming your horse across a larger river should knock a couple of miles off the day’s journey, other unique obstacles might have a similar reduction. (as a guide remember a horse walks at around 4 miles per hour (compared to a human average of around 2.5 - 3mph) so if the obstacle takes half an hour to deal with thats a couple of miles lost.

Out of interest
The Tevis cup is a 100-mile-in-one-day competition which goes over some quite rugged and mountainous trail terrain in the western states of USA... but they do it on very special arab horses, with little or no baggage and even the winning times are usually around 17 hours! link