There are many factors to be taken into consideration.
The fitness, size and type of horse and the terrain.
A Shire, or any of the heavy draught horses are designed for pulling rather than riding yet they would not be suitable for pulling a cart for mile after mile at a trot, they are 'plodders' and most of their work would be done at a walk as in pulling a plough or other farm implements. Yes, they can and do trot when hitched to a wagon but not continuously.
A horse bred as a carriage horse is lighter boned and can keep trotting at a steady pace with a cart, for hours yet would be exhausted pulling a plough for half a day.
A horse pulling logs in forestry has a harder job as it is dead weight and over rough terrain.
In the old days when coach and four were the common way to travel, pre Queen Victoria the average speed was 7/8 mph 11/13 km/h winter, 5 mph 8 km/h
Road improvements upped the speed to 10 mph 16 km/h buy horses were changed every 10-15 miles.