The brindle coat pattern is occassionally caused by a rare genetic occurence called chimerism. Dunbar's Gold, pictured at left, is an example of this odd phenomonon. In a nutshell, a chimeric horse develops when two non-identical twins fuse into one embryo in utero. Dunbar's Gold, therefore, has two sets of DNA, resulting in his brindled coat.
That is the horse that you posted a pic of. Here are some more that I found. The bay in the 4th and 5th pic was a hunter jumper with some success. He is a Brazilian warmblood. I think that brindles are beautiful. They are just so unique.
As far as I knew they're not really sure of the genetics of Brindle actually. It seems to be slightly inheritable from what I've heard. The Brazilian Warmblood that you showed is a stallion and apparently one of his was born with some brindle patterning but it appears to be fading (although we all know how foals coats can be a bit misleading at times) but heres what it looked like when he was born: