If 1 day ride was x miles, was 1 week ride 7x the distance or did they ride 1 day and rest the next?
Compared to Roman times did the distance change greatly?
There are so many factors involved in determining the distance a horse can travel in a day. The horse's breeding is a huge factor in how far and fast it is able to travel, heavy draft animals are slower but steady while thoroughbreds are faster but wear out quickly. Cross breeds are all over the.map in their endurance capabilities. Age and physical condition of the animal are important factors as are the quality of feed available and amount of drinking water along the route. You must also consider the length of the trip and number of days you will be travelling and the terrain as hills and water crossings will slow you down.
An average horse can walk at 4 miles an hour. With prodding you can bump this to around 6 miles per hour. It can trot at speeds ranging between 10 and 15 miles per hour for an hour or so at a time.
So in ideal conditions with water stops along the road a horse in Prime condition can walk about 40 to 50 miles in a ten hour day. If it is in top condition and has lots of high protein feed it should be able to maintain its weight and health. If the feed quality is lacking it will soon start losing weight and won't be able to maintain this pace. An average horse in good condition should be able to cover between 30 and 35 miles in a ten hour day on a good road. If the trail has rivers and hills to cross the distance it can cover in a day begins to drop.
A hard days ride would include a mix of trotting and walking. Pushing it horse this way it would be possible to cover 60 to 70 miles over a ten hour day.
While horses can run at speeds over 30 miles per hour, forcing a horse into a gallop would be counter productive. Most horses are unable to travel at a run for more than two miles and would quickly play out.
The Apaches were renown for their abilities to cover vast distances on horseback. It was not uncommon for them to travel over a hundred miles in a day or even twenty miles further. But these horses would be worn out at the end of the day and many died during or at the end of these runs.
You could extend your range and help maintain your horses health by bringing another horse along. Switching back and forth between them gives your mount a bit of a break which would keep them in better condition over a long trip.
Bringing a packhorse along greatly reduces the distance you can travel in a day if you care about your animals. A rider if fluid moves with the horse as it walks while a pack is dead weight that hangs off each side. Pushing a pack horse to a fast walk will cause it to get saddle sores. The rubbing action of the saddle and pack against the horses side will rub through the hair and creates blisters. Most pack trains seldom travelled more than 18 miles in a day while 12 to 15 miles was the norm.
I have not run into this in primary sources dating to the nineteenth century. It does occur in later primary sources - movies and TV - but these have nothing to do with the actual West. Movies and TV are accurate primary sources when attempting to understand the "Wild West," a place that did not exist in the nineteenth century.
In 1859, Hank Monk drove Horace Greeley across the Sierra 40 miles in four hours, but that was on a road that, while not perfect, was at least prepared to a certain extent.
Riding in a wehicle drawn by a team with horses changed every ten miles (every hour) is one thing, riding a horse is another. Similar surprising feats of speed were achieved by the Pony Express, but here again, riders changed horses throughout their ride as they covered considerable distances in a single day.
How far one could travel in a day on a single horse depended a lot of terrain, and the West is a very large place, so the answer to your question could vary a great deal depending on the circumstance.
People still talk about a certain town being "an hour away." That is understood locally because people tend to decribe the distances they know in terms of time rather then miles. That said, "an hour away" means something very different when considering traffic issues in the Los Angeles area (where "an hour away" might mean 5 miles away) as opposed to that same time in the rural intermountain West (where "an hour away" may translate into 70 miles). There are many Wests, and the asnwer to your question would depend on the local situation.