What are the pilgrims using for transportation?

You don't always get a description of the horse, but the pilgrims are riding on horseback to Canterbury. The General Prologue mentions the need for stables, and several of the pilgrims are actually specifically described as being on horseback. The Oxford Clerk, for example, specifically described as being thin, rides on a very thin horse. The Cook, in the prologue to the Manciple's Tale (toward the end of the tales) actually almost falls off his horse.