Going-to-Sun-Road often doesn't open until around the 4th of July.
The Going-to-Sun-Road tops out at 6,647 feet and in July and August there is still usually quite a bit of snow at that elevation. Join the myriad others who are making the journey over one of the most beautiful stretches of asphalt in America. It is not uncommon to find many other skiers and snowboarders with the same idea, but there is a wide array of terrain in these parts so getting your own little corner of this expanse shouldn't be a problem.
Park in the Logan Pass visitor center parking lot (or better yet, catch a lift in one of the Glacier National Park shuttles) and head off down the Hidden Lake boardwalk. Depending on snow levels you may have to boot it for aways. Pay extra attention to the delicate flora in this region and do NOT ski or walk on anything but the boardwalk or snow surface. Heed any posted signs the NPS may have present.
Exit the Hidden Lake trail and make your way to whatever starting point you'd like to peruse in the "Hanging Garden" snowfield. Enjoy corn turns and huge blue skies.