The are available at POR. On another thread, a poster said that they were $30 for a half hour. We're planning on trying it out in early February, with a blanket in case it's cold then.
Private carriage rides - Cost $30/half-hour. Call (407) 824-2832 to reserve (reservations suggested, not required). Depart from Crockett's Tavern at Pioneer Hall between 6 p.m. and 10 p.m. nightly. There are two carriages available; one accommodates four adults and two children, the other accommodates two adults and two children.