Aaron Rodgers' awesome offseason kept right on rolling on Friday ... as he seemed to have a helluva time at Churchill Downs, smokin' stogies and hanging out with his good pal, Davante Adams!

The New York Jets superstar hit up the venerable race track in Louisville for the Kentucky Oaks one day before the Kentucky Derby went down ... and he looked like he was having a blast.

He was spotted enjoying a cigar -- and chatting it up with a bunch of famous people ... including Adams, who he was teammates with in Green Bay for nearly a decade.

One witness tells TMZ Sports ... Rodgers looked quite relaxed during his time in the luxury suite -- chillin' out and watching the horses with his friends without a care in the world.

As for his surgically repaired Achilles, we're told no one noticed any kind of limp as he made his way around the venue.

It's, of course, the latest fun day for Rodgers this offseason ... as last week, his Jets got him a big-time offensive lineman, Olu Fashanu, and a fun wideout, Malachi Corley, in the NFL Draft. And, just days earlier, he got to rekindle his bromance with Jets star Garrett Wilson.