Usually, a rain to snow scenario involves a changing of direction in the winds, and when the winds shift to the NW, that will bring in the cold air but it also brings in dry air and shuts off the precip. A lot of our snow-to-rain scenarios involve an established cold air mass where the storm track doesn't necessarily matter, because the initial cold air is enough to overcome the initial push of warmer air. Eventually, the warm air wins out. This past weekend was like a very poor man's example of that, but had a bigger batch of precip and heavier precip been aimed in our direction, we could have done pretty well with that. Same thing can also happen with coastal systems if they are too close. We can begin as snow and then switch to sleet and even rain as the winds become too easterly/southeasterly.
IIRC, 2011 was a strong upper level low that did create its own cold air. Once we got on the back side of it, we switched over to heavy snow. I love that storm. Just wish it had lasted longer. It really crushed some areas northeast of us. Talk about a heavy thump though, especially of very heavy, wet snow.