You might want to check with the Forest Service. Up the Shields River on the east side I recall seeing the Sunlight Lake trail signed as something like "unsuitable" for "not recommended" for stock use. Ditto the trail to Blue Lake from off the Big Timber Creek trail on the east side. Those are just the ones I happened to notice so there may be others. The ones mentioned go up to and above timberline with lots of loose rock scree slopes.
I haven't ridden or packed in many years but my neighbor still does and we've been discussing the idea of taking in a camp with his mules to the very top northwest corner of the Crazies (head of Indian or Sawmill Creek) from the Forest Lake road off of Hwy 294 to Martinsdale. The trails up there are mostly old logging roads and two-tracks, they close them off to all motorized on Sept 14th, and there's essentially no public access from the north, east or west. IIRC, pretty much all the private around it is outfitted. Area consists of nice pockets of dark timber interspersed with some rather large meadows and open, grassy ridge tops. It's on our bucket list but we haven't actually gone up in there during season yet.