Do you mean Tenaya Lodge? That's just south of the park on CA-41. YARTS will have their winter schedule up eventually.
It's at high enough of an elevation that there could be snow. However, I wouldn't expect that you would need chains. I've been there in the winter, and didn't see any snow on CA-41 at all, but did see people chaining up their vehicles before entering the park. There was a chain requirement on Wawona Road when I saw that.
The YARTS buses should be OK in winter. I believe they have chains if needed or may use winter tires.