A post on the The Red Lodge Area Chamber of Commerce Facebook page made it official:

The Beartooth Highway will be closing for the season early in the morning on Friday, October 5th. This early closure is due to the inclement weather that is expected through the next several days. This closure will be from Red Lodge to Cooke City

Until the re-opening in the Spring of 2019, the Chamber suggests taking the Chief Joseph Highway as an "amazing alternate route."

"Makes me sad! I love this drive. See you next summer Beartooth Highway!"  -Chris Leedy Ross from Facebook