A main goal of the Continental Army was simply to exist. Washington's war being one pretty much centered on a Fabian strategy, tying the British down and seeking to fight only when nessessary. As a result of this and as others noted, the massive resource drain of building a real mounted arm, there's little reason for such a force to exist.
At the very least its hard to imagine that amid all the supply struggles and cold winters such a force could continue to operate. Furthermore, its difficult to see that issues of food and mounts aside, what benefit it would bring. There aren't many duties that the Cavalry would provide that weren't already covered for Washington. Militia, Rangers, Riflemen, and Light Infantry could cover the scouting and flank fighting the Cavalry normally was assigned, and Scouting and Intelligence could be covered by the same men, and by the widespread network of ideological Patriot's who could report sightings.