If travel time is less than what the horse takes off, then you arrive in 12 hours.
Horse - You arrive 8 hours early. Cost - 3,000 (z)
White Stallion - You arrive 12 hours early. Cost - 8,000 (z)
Horse of the Thief - You arrive one day early. Cost - 15,000 (z)
Horse of the King of Thieves - You arrive one day and 12 hours early. Cost - 30,000 (z)
Emperor's Royal Guard's Horse - You arrive 2 days early. Cost - 50,000 (z)
Emperor's Horse - You arrive at your destination 2 days and 12 hours early. Cost - 75,000 (z)
Carriages-
If travel time is less than what the carriage takes off, then you arrive in 8 hours.
Common Carriage - Carry's 2 people, takes 1 day off travel time. Cost - 15,000 (z)
Luxury Carriage - Carry's 4 people, takes 1 day off travel time. Cost - 30,000 (z)
Speed Carriage - Carry's 2 people, takes 3 days off travel time. Cost - 95,000 (z)
Royal Carriage - Carry's 4 people, takes 2 days off travel time. Cost - 85,000 (z)