Squaw basin is a little-known feature hidden in the Western Wallowas that provides a variety of ski options. Squaw Butte offers some some eye candy for skiing, but the trick is hitting up the slopes at the right time. The wide open slopes on the west side of the ridge are extra exposed to sun and wind and coverage lower on the mountain can be sketchy. All in all, it is relatively quick access and awesomeness that makes it worth visiting.
The main tour route into the basin affords more options for skiing. It mainly follows the summer trail. Use this route with caution because you are hiking under some high angle slopes; however, the initial mile has mature trees and not as much weight above you so it should be good. The eastern side of the canyon shows more signs of big avalanche activity. The alternate route shown here travels straight up the spine, from south to north. The initial climbing is steep and the ridge is a bit tricky when first cresting, but the travel becomes easier as you move north.
Access
Park in the parking area on the west side of Hwy 203 across from NF-7785 (Catherine Creek Ln. toward North Fork CG). This is not a SnoPark so permits aren't required, but it isn't plowed regularly so it can be hit and miss for parking. Alternately, drive up Rd 7785 east from the highway. It is plowed for about a mile to the camp and you can park on the side of the road where it widens by the camp. The snowmobile ride is not that technical, other than a stream crossing. These aren't heavily used snowmobile trails and they are not groomed so you might experience some downed trees.
Take a quick snowmobile ride along Catherine Creek to North Fork Trailhead. Then, to get closer to the described route you have to cross the creek on the newly installed bridge from 2014.
By car, you could try to forge down this road, which is relatively flat all the way to the trailhead. You'll likely have to park at the North Fork trailhead if you make it that far, and head up the road by skis which will be a long slog on the road but you won't have to put skins on for the ski out when you're done.