Video doesn't show much the mud masks things a bit but from your description I suspect a spinal lesion. They walk in straight line OK but the change in direction the back legs still go in straight line just don't follow the front. The video does show a bit of an exagerrated gait. In placing their leg instead of going from A to B directly they go via C, lacking fine motor control usually from some pressure on the spinal cord. This is like what you see in Dachshunds when they have a partial prolapse of the disc.
It may only be bruising and things improve as the swelling goes down but also could be more permanent damage. Not much you can do other than rest and keeping him away from others but I don't think confining him in those muddy conditions would help. Corticosteroids are always usefull in spinal conditions in helping to relieve the inflammation, Dexamethasone is only a short duration and would have to be given daily, there are other longer acting steroids like Triamcinalone Forte which is a good one for spinal lesions and will last 5-7 days.
Ken
