Just did my 4th trip up the west side of GTS to Logan Pass back in June during a two-week tour in the state. You have to check the park's official web site. Typically there is a drop dead closure date for construction activity. This year the west side will be closed starting October 9th, assuming weather doesn't close it earlier:


https://www.nps.gov/glac/planyourvisit/gtsrinfo.htm


Some years, the closure date has been in September. If you go in late September/early October foul weather gear is essential. I have been up there in cold and wet conditions. It's something you want to be well prepared for, particularly at that time of year. This year I rode up the west side and back down on 6/28. Despite it being sunny at the pass, I needed to put my windbreaker and leg warmers on. Don't be surprised or disappointed if it snows.