Win 7 officially goes out of support in mid-January. That doesn't mean it stops working or that applications like TS3 running on it instantly stop working just then. But potentially it does become a security risk for computers that face the Internet in any way as there will no longer be any Windows Updates to it (except possibly for emergency ones, XP got a couple of those post-support). Eventually applications and web services will stop supporting it, web browsers and plug-ins will no longer account for Win 7 users, etc. so there is an unknown timing element. In theory Origin could stop supporting Win 7 and some future update could break it unintentionally without anyone at EA realizing it until users complain (and then they won't likely fix it). We would expect an announcement from EA as to when the dropped support and testing might happen, though. I doubt they test and support Vista any longer, for example, but I'm pretty sure at least some time passed before that happened.
If you have a disc install and are not relying on Origin or online in-game services, this doesn't really matter quite as much.
Best practice would be to plan to upgrade to Win 10 at some point, if one's hardware can tolerate it and with the understanding that sometimes upgrades do not function as well as they should and the user may need to wipe their hard drive (thus losing everything that is on it if it's not backed up somehow) and install Win 10 fresh from scratch.