If it is horse drawn or pulled by an animal, it is similar to car, but because drawn by an animal, more suggestive of a direction brought about by biological drives such as sex and ageing. Can depict how you are dealing with such drives. Or it might depict a special occasion such as marriage or a funeral – but the biological process of change also underlies these. See: car.
If it is a train carriage see railway.
Useful Questions and Hints:
What is carrying me or pushing me along in life, and what do I feel about it?
Is there a change happening in this dream, and if so what is it suggesting about my life?
Am I involved or an observer of this? If an observer what am I understanding?