There are several low-elevation trails on the east side of the park that are usually safe to hike in winter. The snow is generally too deep for hiking west of the Continental Divide. Of the trails described above, Cub Lake Trail, Gem Lake Trail, and the first part of the Fern Lake Trail, to the Pool, are all reasonably passable in winter. Two other relatively short trails are also recommended.
You can access the easy 3.5-mile Upper Beaver Meadows Trail from a closed gate on the west side of Upper Beaver Road, about 2 miles west of park headquarters. Inside the gate, a trail forks to the left and a road forks to the right. They connect at the other end of Beaver Meadows, so you can follow either of them. The trail crosses Beaver Brook and skirts the south side of the meadow, eventually bending north to meet the road in the parking area at the west end of the meadow. The road winds through the meadow north of the brook, and back to the starting point. Watch for elk near the water or at the edge of the trees. The initial elevation is 8,300 feet, with an elevation gain of 140 feet.
The other recommended trail for winter hikers is the moderate 2.5-mile Chasm Falls Trail. To get to the trail head, turn west onto Endovalley Road off U.S. 34 at Horseshoe Park and drive to the road closure. From the parking lot, hike along Endovalley Road for about 1.5 miles to Old Fall River Road. Watch for ruins of the cabins where the prison laborers who built Old Fall River Road in the early 20th century lived. Head up Old Fall River Road (the right fork) about a mile to the falls. As you approach the falls, you'll notice lovely, but treacherous, ice formations -- proceed very carefully. The beginning elevation is 8,960 feet, and there is a gain of 400 feet.