Palfrey – a compliable horse for casual riding, especially by women.
Mule, hinny – the offspring of a male donkey and a female horse, usually sterile and used as a beast of burden.
Dray horse, draft horse, cart horse, sled horse – a burly and formidable horse for pulling drays, carts, buggies, sleds, etc.
Rounsey, rouncey – an all-purpose horse, able to be trained for war if needed.
Courser – a swift or spirited horse, in any application.
Destrier – a medieval knight’s horse for battles or tourneys.
Warhorse – a big, mighty horse trained for war, whether it be modern or historical.
Mount, steed – a horse being ridden or is available for riding.