Three miles of easy hiking on Whitepine Creek trail leads you to Wildhorse Creek Trail. 6.5 on the Wildhorse Creek trail takes you due south to Frosty Pass, Icicle Ridge Trail, and Frosty Creek Trail. It accesses Lake Grace, Big Chiwaukum, Snowgrass Mountain and Doelle Lakes through wide open high country.
One can do a loop, beginning with Whitepine Creek and heading to Wildhorse Creek, the up to Frosty Pass on Icicle Ridge. Continue to Chain Lakes to connect with Icicle Creek before returning to Whitepine Creek to round out the hike. The crux is the Whitepine Creek ford a few hundred yards from the Wildhorse junction, which may run high, so check it out before you commit to it; by late July or August, it should be a safe boots-on wade with a good stick near the ruins of the old bridge. Maybe tricky at high water.
You'll start by buying your altitude on Wildhorse passing through white pines, and soon clear timberline at about 5000 feet in about 2.5 miles. There are at least two established campsites at permanent streams along the way, found in the trees.
Below and west of Lake Grace, the trail descends into a brushy section, about 1.2 mile. This does not last. After crossing some obvious avalanche/flood debris, you'll find the signed junction back to Lake Grace. Note that this is well past the Lake Grace outfall stream.
Lake Grace has established campsites. The more adventuresome may scramble to a more alpine environment at Upper Grace Lake, found at 6900 feet.
Although the ascent of Big Chiwaukum's true summit requires some careful Class 3 climbing with loose rock, from Upper Grace Lake one can get quite high with hands-free walk in an alpine setting along an inspiring, wide-open, easy ridge, reaching 8000 feet with stunning views.
It's a horse trail, so there are some rocky and eroded sections, and it doesn't get a whole lot of maintenance, so it's brushy in places, but on the whole it's a reasonably easy easy trail.
At Frosty Pass (5700') is a 4-way junction. Frosty Creek Trail drops southwest to Lake Margaret and Icicle Creek Trail. Alternately, the Icicle Ridge trail climbs southeast to Lake Mary, Mary's Pass, Upper Florence Lake, and Ladies Pass. There are two "Lake Mary Hiker Trail" signs; if you want to camp above Lake Mary, disregard the first and find two established campsites close by the second sign at 6200 feet, over 100 feet above the lake. Above the trail near Lake Mary, note the odd, straight east fork of Frosty Creek which flows west into Lake Margaret; it drains a flat basin at 6500 feet, a subalpine wonderland.
From here, one may wander north, then east in steep terrain to the 7420-foot saddle on Snowgrass Mountain's south ridge. To reach the true 7993-foot summit, you must traverse on big snowfields, which are scree when snow is not present, on the east side before ascending, but if "close" is good enough for you, the south ridge is a simple amble on alpine tundra (tiptoe carefully!) to a gendarme that will stop you above 7800 feet.
For the adventuresome, Icicle Ridge Trail continues northwest of Frosty Pass, unmaintained, to Doelle Lakes, over a pass, to Chain Lakes Trail. Follow the two "Horse Camp" signs at Frosty Pass, and just continue past the horse camp in mostly open country. Shortly after this trail crosses to the southwest side of the ridge, an obscure path leads north-northwest through a 5550-foot notch into wide-open hill country between 5000 and 6000 feet; perhaps this is an old sheepherders' path?
If you complete the loop via Icicle Creek Trail, you'll exercise your trail sense to find and follow upper White Pine Creek Trail: there may be a junction sign, but the path disappears into a lush meadow, so you'll look for an old blaze on the other side. Monster cedars in the bottomland will silence you.
If you brave some snow and go here in June, you'll be rewarded with more attractive, snowy terrain. It looks more barren and severe by September. Be aware of high hunt season in late September. Careful cross-country travel is possible, but tread lightly and be sure to follow Leave No Trace guidelines.