From Shrine Mountain Inn climb SW 1 mile and 531 vertical feet to Shrine Mountain Saddle (11,740 feet). This is the first saddle southeast of Shrine Mountain. Enjoy the awesome view of the Holy Cross Mountains and take the time to evaluate your position. For the next 1 1/4 miles the trail stays above timberline, skirting and gradually dropping around the west side of Shrine Mountain Ridge. In poor or deteriorating weather you should consider turning back.
Continuing from Shrine Mountain Saddle, use your compass, map, and altimeter to make an accurate dropping traverse to timberline on the southwest face of the ridge, on the north side of the Wearyman Creek drainage. From here you can ski directly down to the apex of the drainage at 11,000 feet or take a more gradual dropping traverse SE into the drainage. With good snow you can make some fine turns with the former option. Novice downhillers should stick to the latter.
At 11,040 feet in the Wearyman Creek drainage you'll be in an elongated park. Near the lower (west) end of the park find the channel where Wearyman Creek leaves the park. Here you'll find the marked 10th Mountain suggested route. It crosses to the west side of Wearyman Creek for a short distance, enters the trees on a trail that may be packed by snowcat, and drops down a steep hill to a small clearing. From the clearing stay on the 10th Mountain suggested route as it climbs SW through forest for a short distance to a distinct logging road (10,880 feet). Follow this road SW 1 3/4 miles to about 11,200 feet, where it begins to climb SE via a series of low-angled, inefficient switchbacks. If you're using wax you might like these switchbacks. Many skiers, however, put their skins on and cut directly up the hill, use the switchbacks for reference, and regain the 10th Mountain suggested route at the last switchback.
Whatever your choice in routes, once you gain the ridge at the 11,460-foot level (Ptarmigan Ridge), follow it W then SW 1/3 mile to the Fowler/Hilliard Hut. You can not see the hut until you reach the small knob several hundred yards southeast of the site.
There is a good variation for this route that gives you a lot more high altitude ridge-running and alpine feeling. Simply stay on Shrine Mountain Ridge all the way to the saddle that divides the Wearyman and Wilder drainages. From the saddle climb S to Ptarmigan Pass, then ascend the ridge W to the summit of Ptarmigan Hill. Drop down the west side of Ptarmigan Hill to a distinct road-cut. Ski the road W as it skirts the south side of Ptarmigan Ridge and then intersects the 10th Mountain marked route leading W along the ridge to the Fowler/Hilliard Hut. Only use this route with excellent weather.