According to the latest Trail Status update on the park website, the trail to the Granite Park Chalet from the Loop, is now open. As of Monday, snow cover on the trail was noted as being >1%.
The Highline Trail from Logan Pass, however remains closed due to snow. The trail is expected to open on 8/3/12.
The trail to Sperry Chalet from Lake McDonald is cleared to within a half-mile of the Chalet. According to the latest report there are 2 trees down, and the trail still has 15% snow cover. However, according to the most recent posting on the Sperry Chalet website:
"the first adventurers to try (hiking it) have reported it to be challenging but passable. You will want to bring some trekking poles and extra traction for your shoes if you want to attempt Sperry Glacier soon. Lincoln Pass to Lake Ellen Wilson still has significant snow cover as well."
If you wish to visit the chalet via the Gunsight Pass Trail, please note that:
"We would advise avoiding the Gunsight Pass Trail for the month of July. We do not yet have any good firsthand accounts of conditions at Gunsight Pass, but historically we know that when these snow conditions exist in the high country, there are some extremely dangerous snow crossings on the east side of the pass. If you want to attempt it, we recommend climbing gear, ice axes, well practiced self arrest skills, and experienced hiking buddies. Be safe out there."
Glacier National Park Hiking