Horses

Horses are of great utility off the battlefield. In the Empire, there is no faster and more reliable means of transport than a horse – even some river barges are drawn by horse or mule, plodding along the edge of the river. Farmers yoke teams of draught horses to their plow, and Strigany wanderers travel in horse-drawn caravans. Roadwardens take especial care of their mounts, as being unhorsed in the more hazardous portions of the Reikwald can be a death sentence. Adventurers, too, will find many reasons to love their steeds. A horse can carry bulky items that would weigh a human or elf down (not to mention the adventurer himself), horses can travel further and faster in a day over level ground than a man on foot, and, as nearly every fighting force in the Old World has discovered at one point or another, there are many advantages to fighting from horseback.

In the Old World, almost everyone has at least some knowledge of horses. Even a character with no training can mount a horse and point it in the right direction. Basic tasks such as riding along a level road at a walk require neither training nor a check. Maintaining saddle and tack, feeding and grooming a horse, and dressing a horse for work or battle, however, are more specialized skills that would generally require training or a natural skill – thus the widespread use of grooms, farriers, and squires.

Concerning Dwarfs
Dwarfs are a proud, stubborn folk, much bound by tradition and suspicious of change. They are also a mountain dwelling people, who build great cities beneath the earth, and as such do not have much use for horses or other mounts, except as beasts of burden or labour. It is, in fact, a point of dwarf culture that Dwarfs do not ride. Why don’t dwarfs ride?

Because they don’t and that’s all there is to it!

Unlike humans and elves, dwarfs have no tradition of horsemanship in their culture. Obviously, they’re physically capable of riding; although they are rather too small for most horses, a dwarf could do quite well on a suitably sturdy pony. Rare indeed, however, would be the dwarf capable of overcoming the weight of generations of tradition of not riding to mount such a beast. Any party attempting to travel at speed with a dwarf in tow is well-advised to invest in a wagon or carriage, where the dwarf will be much more comfortable.

Suggestions that dwarfs don’t ride because they are afraid of horses are not advisable, and will likely be met with a new entry in the Book of Grudges.

Source
pg. 42 43
 * Warhammer Fantasy RPG 3rd ED -- Omens of War