I have exchanged a few emails with both Wildcat and the Forest Service. Here is a summary of what I have been told.
From Wildcat:
Wildcat does not wish to deter hiking.
The uphill ski pass is designed for folks that want to hike/skin up and ski down the mountain.
Downhill hikers are asked to check in with the ski patrol before descending to be sure it is safe to do so.
Sledding is not allowed
Access on the ski trails is not allowed outside of operating hours
When asked about dogs, snowshoes, etc.. I was refered to the Forest Service.
From the Forest Service:
Ditto to what Wildcat stated above.
They have 121 ski areas on Forest Service land across the country so need to be in sync across the country.
Dogs are not allowed on the ski trails as they would post hole and leave poop on the ski trails.
Snowshoes are not required.
A hiker who does not plan their hike correctly and finds themself at the top of the ski slop after hours would be allowed to hike down as this would be a safety item.
One thing I find hard to believe is that they think a dog will post hole more than a 200 pound hiker without snowshoes. I could see it if they requried hikers to use snowshoes or skis, but that is not the case. Also seems like they are punnishing all dog owners for the few that may not pick up after their dog on the ski slope/trail.