@NC-Retired
Again, sustained, day on day travel by a horse in good condition, no HUGE rider, noexcessive loads, no extraordinary need to kill the horse to get the human to some location.
Again, a lot depends on what you consider an excessive load.
Consider rider around 180 pounds. Full USMC combat pack is around 100 pounds. I would not consider that excessive for wilderness or deep rural conditions.
300 pounds would not be excessive for a horse that is breed for riding and physically fit.
Walking the horse - 4mph - can a well conditioned horse maintain this pace for 10 hours with 14 hours to rest and feed, thus a 40 mile day?
Possibly, but you need to account for more than just travel time.
The rider needs time to in the morning, feed himself, feed and water the horse, pack up his camp, and at night to set up camp feed himself, feed and water the horse.
Assuming you are planning to let the horse graze, it will need 16 to 20 pounds of food per day. That will take longer grazing wild grasses than eating hay that you gathered and piled up.
What is the rider going to eat? Does his food need to be cooked? What's the climate/weather like? Will the rider need a fire for warmth?
That means time to gather fire wood and start a fire. What tools does he have to start a fire? A butane lighter? matches? Flint & steel? Or does he have to rub two sticks together?
You will almost certainly have to make at least on stop mid day to let the horse drink. Possibly more often depending on weather.
What season and what latitude? How long is the day in local time? Does the rider have a light source, or does he need daylight for his morning and evening activities?
How long will all those other activities take?
Half walking and half trotting the horse - 4mph & 10mph - for 10 hours with 14 hours to rest and feed, thus a 70 mile day?
What's the total distance you need to travel?
That kind of pace could be maintained for a few days, but if you are talking about several weeks of travel, probably not.
Again, considering conditions and ancillary activities, is 10 hours of actual travel time realistic aside from possible effects on the horse's health. And don't forget that the harder you push the horse, the more it will need to eat and drink.
What's the total distance to travel? How many days at each pace? Assuming you aren't limited by availability of daylight, if the ancillary activities needed to maintain horse and rider take up more than 6 hours a day, how long can the rider go on whatever amount of sleep?