The answer will depend on what you mean. If you mean an exact name, there is no way to answer that without knowing the horse. If you are asking if a brown and white pinto mare is called something specific, then no, she would still be a mare.
palomino
a horse
The quagga is a now extinct subspecies of the plains zebra. It had a unique coloration pattern, with white legs, a brown body, head and neck, and white stripes on the neck. A mare would be a female quagga.
Unfortunately your question is not specific enough about the colors of each parent horse. By white...do you mean a truly white horse? Such as one that carries dominate white, or is it maximally expressed sabino causing the white? Or is the mare actually grey with a white coat? As for the stallion what 'brown' do you speak of? Is it bay, brown agouti, or chestnut? And what is he homozygous for exactly? Is he a tobiano or another pattern. Without this exact information your question cannot be completely and accurately answered.
The child of a mare is called a foal.
The mother of a mare is called the dam.
Most likely not. Rain is thought to be a pinto mustang or Indian pony mare.
This completely depends on the ancestors of both of the parents for instence my friend had a black stallion and a white mare but her foal came out brown. this is because the mare's mother was brown, basically the brown gene from the "grandmother" skipped one genaration but was still in the white mares blood and so it was passed onto the foal. Genes can infact be passed on up to five generations down the line. hope this helps!
A mare is a full grown female horse. An adult mare is called a mare. It is sometimes used as a euphemism for a married woman.
A female horse is called a Mare baby horse is called a Filly
Pinto is a color and not a breed. Therefore a pinto colored horses production can vary greatly. But for horses in general they can produce and average of one foal a year per mare, with stallions helping to produce many more than that.
A stallion's mate is typically called a mare.