(No Spoilers) An (Updated) Guide to the Horses of Westeros
Adding some things that /u/Syrele left out.
DESTRIERS
PALFREYS
COURSERS
ROUNSEY
GARRON
ZORSE
SAND STEED
STOT
Geldings - Male horses that have been castrated. They are as strong as stallions, but less temperamental and moody.
Mare - Fully grown female horse
Stallion - Fully grown male horse
Foal - Baby horse.
Colt - Young male horse.
Filly - Young female horse.
http://www.reddit.com/r/asoiaf/comments/1bi66i/no_spoilers_an_updated_guide_to_the_horses_of/