Different horse will have different endurance levels. Some horses can only move fast for short periods of time, others for long periods of time, e.g., the Arabian.
Trotting is slower than the gallop, but trotting for long periods of time is actually better exercise.
The miles that a horse can trot a day depends strongly on that horses fitness, breed, age and conformation. That is a question that has more than one answer, and it highly depends.
Hope this helps a bit,
Winnie the Horse Gentler
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