Start at the Pando TH and ski E across the main north/south Camp Hale Road, across a bridge over the Eagle River, then E and NE to intersect a snow-covered road running north/south at the base of the mountain.
To avoid snowmobile traffic do the following: Ski the north/south road at the base of the mountain N a short distance, then turn right and ski SE up through a gulch east of point 9,540 (again, this is not the main Camp Hale Road). One mile from Pando you intersect the distinct Resolution Road. Take a left (NE) and ski 2 1/2 miles up the Resolution Road to 9,960 feet.
Leave the Resolution Road here and take a left (NW) onto a marked 10th Mountain trail. The blue diamonds take you up 980 vertical feet to a 10,940-foot saddle on the southwest ridge of Resolution Mountain. Most of this trail follows a distinct trail-cut through forest. In the occasional clearing take the time to zero in on the route with your map. Climb the southwest ridge of Resolution Mountain 3/4 mile to 11,400 feet (you'll pass the intersection of route 9.1 at 11,300 feet). Next, take a 3/4-mile climbing traverse NE then N across the west face of Resolution Mountain, ending at 11,700-foot Resolution Saddle on the northwest ridge of Resolution Mountain. Ski down E from the saddle and cut a short traverse that leads you to a distinct east/west cleft called Resolution Narrows. Continue E down Resolution Narrows to the Fowler/Hilliard Hut in a clearing at 11,500 feet. In clear weather the hut is visible from Resolution Saddle. For "bonus turns" consider ascending Resolution Mountain, then cutting turns down to the hut.