Well, I took pics of the tracks yesterday, but couldn't get a good one.  I'm going to try the new tracks tonight, after the sun goes down - maybe I'll get a better outline???  The tracks this morning were definite cat-like, small, round in nature.  The tracks yesterday appeared to have a drag of some sort, but couldn't tell if they were because of the snow or because of the foot making the track.  
The door to the coop is on a lock with a 2x4 surrounding it, to bar against prying the door open.  The door to the run is on a slide - from the inside - so that when it's shut nothing can push it open.  Inside the coop, there are two rooms - a feed storage and the coop.  The outside door opens to the feed storage, but everything is in sealed cans.  The coop door is a half door with no wire enclosing the opening.  But again, I don't see any holes or openings that would allow a predator to enter the feed storage area and it is checked at night before we lock up the chickens.
We had a problem with rats last winter, but we built a new coop and the old coop was torn down (pretty rickety) and bait was set out for the rats.  No problems all summer long.  There are a few tunnelling holes into the garage, but they look smaller, like field mice.