I think keeping everybody together was the real reason. Also Frodo wouldn't leave his friends in danger and only mounted when Glorfindel convinced him that they were less in danger if they weren't with him.
I will try to be that expert! I am an active trail rider who owns a retired endurance racing horse.
When my horse was racing and in peak condition, he did 100 mile races in a day... these are finely conditioned horses, and there are rest periods. The races are done mostly at a medium-to extended trot, not a gallop. Based on condition and strategy, riders give the horses walking breaks periodically over the race course, and there are mandatory rest periods where the horse is not allowed to go on until his temp and heart rate have returned to normal. The better conditioned the horse is, the quicker he recovers and the faster they can get on their way.
Walking for pleasure I do 25 mile rides. A moderately conditioned horse can walk this distance bearing a rider and stay sound. When I did it last summer, we were out 5 hours or so, including stopping for lunch and several breaks along the way, mostly to rest the riders knees and behinds, the horses don't complain as much as the riders do on long rides.
These are guesses, because I couldn't quickly find a speed chart in a google search, but if memory serves:
Walking, a horse moves at about 8 mph
Trotting, a horse moves at about 12-20 mph, this is the most efficient way to go long distance.
Galloping/cantering, I would guess that they could go about 30-45, but not for REALLY long distances, but a reasonably conditioned horse could certainly canter at a good pace (not a full out gallop) for 10 miles...
Asfoloth, of course is an elf horses, and would not tire.
I can't imagine that marching troops could go further in a day than the cavalry horse troops at a reasonable pace.
That is all I know (actually more than I know, if I have erred on my guesses)... but I hope it helps
I think keeping everybody together was the real reason. Also Frodo wouldn't leave his friends in danger and only mounted when Glorfindel convinced him that they were less in danger if they weren't with him.