Passing on information.
Inheriting particular looks or personality is all to do with 'genes'. Genes contain the information that makes every living thing the way it is - in a horse, they 'programme' whether it is, say, bay or dun; calm or high spirited; athletic or clumsy. This information is passed on from one generation to the next.
Think of families you know. There are definite likenesses between sisters and brothers - they may all have a similar straight nose or blond hair. When you see their parents, you can tell where the resemblance comes from: they may have inherited features from their father and hair colour from their mother.

Generation gap.
Within that blond-haired family, however, there may be one who looks completely different and has, say, red hair. This is because some genes can 'skip' generations, and the red hair may have come originally from a grandparent.
The same goes for horses. A palomino stallion may be able to pass on his colour to his foals but, if he carries a chestnut gene from further back in his family, one or more of the foals could be chestnut.
The information in genes also plays a part in programming characteristics of conformation and temperament. This can be used to 'plan' better foals. A long-backed mare and a short-backed stallion could produce a foal with the prefect length of back. But don't rely on two wrongs making a right: the foal could just as easily turn out with the same back fault as one of the parents.

A bit of a gamble.
You can never predict with absolute certainty what a foal will be like - breeding horses can be a real gamble. A foal can have pony - sized parents may produce a dark chestnut foal.
But there are ways of lessening the gamble. High-quality stallions of known breeding are more likely to pass on their good points to their foals. Combined with the best possible mares, the gamble becomes more likely to pay off.

Combining breeds.
There are many well-known breeds whose qualities are valued for cross-breeding all over the world.
The Arab is one of most beautiful and ancient of breeds. They have been used for centuries to give elegance, endurance and spirit to top-class breeds.
The Thoroughbred, descended from the Arab, is a superb cross with practically any other type. Thoroughbreds add speed and agility. Warm-bloods are very popular as all - round sports horses for dressage, eventing and show jumping. Warm-blood breeds such as the Hanoverian, the Dutch Warm-blood and the Trakehner are known as compound breeds - they are made by mixing Thoroughbreds and Arabs with local carriage horses.
hardiness, cleverness and strength are all qualities found in the native pony breeds of Great Britain. They can make some very successful crosses - and many a Grand National winner has had a touch of pony blood.