The ability to play these games is not going away, though online services like matchmaking will no longer be supported in some cases. Essentially, if it requires the internet, that mode likely won’t be available after January 13th. You can have a look at the chart before for which services specifically are ending on January 13th:
The biggest change is unquestionably the end of online matchmaking for Halo: Reach, Halo 4, Halo 3: ODST, and Halo 3. Interestingly enough, Halo: Spartan Assault and Halo Wars will still keep their online matchmaking, making these the exception to the rule. Service records, challenges, file sharing, and player customization will also be going offline in a variety of games, so take note of that as well.
343 notes that these shutdowns apply to backward-compatible versions of these games played on Xbox One or Xbox Series X. It seems that if you want to continue playing online multiplayer in Halo 3, Reach, ODST, or Halo 4, you’ll need to pick up Halo: The Master Chief Collection on newer Xbox consoles. Halo Infinite, the latest game in the series, is due out on Xbox One, Xbox Series X, PC, and Xbox Game Pass on December 8th, 2021.
Keyword: Halo Xbox 360 games lose online service early next year