Peter,
You would still upset the ground and the plant life with your feet and rub against grass and brush. You certainly would leave less scent than when running full bore breaking a sweat and this would help the track to age faster. If it is fresh (less than 12 h), you are hosed either way if a good set of hounds is on your track.
For example here in the Western US cougars are often pursued with big game hounds. A cat has to be one of the smoothest and most quietly moving mammals out there. Successfully following a 12-24 hour old cougar track and connecting with the animal in cold weather is very common.
George