William's 2,000 horses isn't really much. The Channel is narrow, you don't need hundreds of ships. You would use a normal campaign camp of those days and move from there. There's no long-term planning necessary, all you need is a place to land, your ships can go back and forth and bring the rest.
Cortes, for his conquest of the Aztec empire, only had 100 horses and about 3,000 infantry. No problem moving that amount of troops on his 13 ships for 4-5 weeks.