No, the East side is close, the side that is part of the Native American reservation. If you follow Going-to-the-sun road it will take you a little before St Mary's and then you must turn around.
East entrance is closed so you have to enter through West Glacier and cannot drive all the way through. The visitor center is open and so is the shop at Logan Pass. At least at the time of this posting.
Use their web...
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