Baucus started the cowboy hat tradition in 2001 and has ridden a horse in every presidential inauguration parade since.
On Monday he was accompanied by newly elected Montana Gov. Steve Bullock (D) and Montana Republican Rep. Steve Daines.
Neither Hatch nor Baucus said they coordinated the hat-wearing event.
But Wyden said it was a matter of Westerners banding together. “This was Oregon’s contribution, the Western contribution,” he said.
Jeremy Herb contributed to this story.