In a spiritual sense transport is being carried from one state of consciousness to another.
This change in consciousness is not necessarily by our own volition. Riding either a horse or a vehicle suggests that we are happy to have the changes take place.
The lift in mood can just as easily be due to external circumstances such as a beautiful day or extreme emotion and this can be reflected in dreams. You might also like to consult the individual entry for aeroplane and the section on archetypes in the introduction for further information.