CALL A DOCTORE!!!!!! that might be serious. That or look it up on line.
Blood isn't good. But the white creamy gunk could be your mare is in heat.
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.
amputate the problem
It means that the mare is pregnant.
Generally, if the mare is in foal she will stop cycling. Some mares may appear to show signs of heat even when pregnant although they are often showing signs of submission (urinating in the presence of a stallion or other mare).
urinating alot does not mean your pregnant...however it is a sign you might be even in the early stages you will have frequent urinaton and or tender breast
No, it just means the mare isn't pregnant.
Mare
Nothing
The white horse might represent freedom from your ex, especially sexual freedom. Yet the meaning of the dream does depend on what sort of white horse you saw, as a worn out white farm horse would mean something quite different from a magnificent white charger, and a sweet white mare would have a meaning distinct from that of a white stallion.
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.
Mare nostrum.
Bay Dun Mare: AaEeDndn, AAEeDndn, AAEEDndn or AaEEDndn if it is heterozygous for the dun allele. 50% of the foals will be dun in this instance. If the mare is homozygous then the foals will be 100% dun. If by white you mean grey then 50% of all foals produced will turn grey independant of their initial birth color. Assuming that the stallion is heterozygous for grey (G). If by white you mean dominant white (W) 50% of all foals produced will be white (there is an ongoing debate about the exsistence of the W gene from what I recall). Since the presence of this allele masks other coat color genetics the white parent may carry any assortment of alleles that affect the color of the foal. If by white you mean maximum expression of Sabino (Sb) the foal could have many variations of white patterning from hardly any to almost completely white in conjunction with the various base and dun dilute combinations mentioned.