Talked to Jack at iON performance and he said in cold weather this is fairly common. A few STIs have had similiar problems up here as well.
According to Jack the noise comes from a combination of many rubber bushings holding the rear diff and assembly in place. As far as he knows there is no polyurethane kit for the LGT, but says NVH would go up a lot.
Lithium grease was given as a possible help for the problem.
I don't know if that helps, but it would be nice to hear from somebody that has at least reduced the problem.