Nice to see new vinyl from The Bangles (and a new CD expected this summer). The 45 is "Anna Lee (Sweetheart Of The Sun)" and features new acoustic takes of "Let It Go" and, yes, "Hazy Shade Of Winter" on the flip. You can buy the 7" direct from The Bangles' web store. The Bangles Christmas output has been somewhat limited, so any version of "Hazy Shade Of Winter" is welcome. Good luck finding either the 1983 "Bangle Jangle Christmas" fan club cassette mix or the later fan club CD from 2004 "Holiday In Bangleonia". The 2006 digital Christmas single, "Light My Way", is still available through iTunes.
The single itself is a nice summer tune, well worthy of the Bangles brand. Here's a fan video so you can check it for yourself.