In 28º & wet snow? It's likely a combination of tramlining, and the tires barely being able to hold the road in the first place. I don't think anything is wrong - but I am glad you made it to your destination in one piece.
I might suggest PTM "Wet" if you ever encounter this situation, again. Snow/Ice mode effectively is the same as Tour, except it changes the throttle map to be a little less "jerky". Stabilitrak doesn't change.
PTM "Wet" engages very different features, including timing and fuel at the engine to maintain grip under acceleration. It does intrude a LOT...in my experience, at least, I've found this to be the most stable suite of Nanny's to drive with in less than ideal conditions. Worst I've done was 36º and wet in the ZL1 1LE....
