Apple has released Software Version 2.0.3 for the iPod classic 160GB (2009). According to the release notes, the software offers support for Genius Mixes; no other changes or bug fixes are mentioned. Notably, the 2009 iPod classic 160GB shipped with Software 2.0.2; the prior iPod classic 120GB was last updated to version 2.0.1, and it is unclear whether Apple plans to add Genius Mixes support to older iPod classic models. The 2.0.3 software update for the iPod classic 160GB (2009) is available now through the Update feature in iTunes.
Update: No new updates have been released for prior iPod classic models to add Genius Mixes support.