WW, a filly has never won the Triple Crown--very few even enter. The name you were probably thinking of is Lil E. Tee, a colt. The story you may be thinking of is that of Ruffian, one of the gamest horses ever. I saw it on TV --you could tell the animal was done for-- and reading about it on this link made tears come to my eyes all over again.
http://www.thoroughbredchampions.com/gallery/ruffian1.htm

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Consuelo, horses, like humans, sweat during hard exercise. They must be walked afterwards until they have cooled down and the sweat has at least mostly dried (a good brushing at this point helps, too). If they are "put away wet", they can catch a chill, and will also get very stiff.