Welcome from South Florida and the Reenactors Forum. You may want to post this question in either the railroad forum or cavalry forum, check out the Long Dusty Road section in the forum selections. In the meantime if anybody could help you with this it would be the cavalry expert here, paging @Eric Wittenberg
Welcome from New Hampshire. I don't know specifically about from Vermont to Virginia but they shipped horses all the time by boxcar. Must have been a wonderful kickfest at times.