I climbed Langley on 6/10/11 via Army Pass. The trail was mostly free of snow up until the Cottonwood Lakes Basin, then the snow coverage was pretty solid. All of the passes on the south side of the basin were covered in steep snow. Crampons and ice axe would be helpful, but you could just kick steps without the equipment if you are comfortable on steep snow. The crest from Army Pass up to the Langley was largely free of snow.
If you do not want to deal with really steep snow and want to leave the crampons and ice axe behind, you can take the chute between the Fin and Langley above the highest lake. That chute is largely melted out. Then circle over to the southwest side of Langley to climb mostly snow-free slopes to the summit.
