When the snow is melted out, which sometimes isn't until late July or August if at all, a trail crosses these slopes to reach the saddle, which is about half a mile northwest of Hyalite Peak. Then it's just a hike up the ridge to the summit.
This view shows why it's smart to have an ice axe or at least trekking poles when undertaking the Class 1 trail up Hyalite.
Gallatin Range, MT-- July 2008