Not too sure but the film may well be "A Gipsy Cavalier" which was directed by J. Stuart Blackton in 1922 staring Georges Carpentier and Flora La Breton. There is a scene in the film whereby a post-chaise is trapped in a flooded area. A post-chaise would be used in the same manner as is shown in this image with the coachman riding the lead horse.
OR.