We just would have to hope for a deeper press of cold. All the precip starts as snow, but melts as it hits a warm nose. 3 different soundings from the 12z GFS at this frame:
one approx at Knoxville, one approx. at Carthage, one at approx. Union City:
Each has the characteristic warm nose. (The red line that kind of looks like a person's nose). In the first one (around Knoxville) the nose spends a lot of time above the 0 Celsius line. So the precip begins as snow (the green and the red lines, temp and dewpoint respectively) meet all the way up to around 350 mb (scale on the left side). That means the atmosphere is moist that high up. The little bars on that left side represent forcing and the dashed, bracketed area labelled DGZ is te zone where dendrites (snowflakes) can grow. If there is moisture in that, you have snow. But it falls through the area where the temp is above 0 celsius (32 Farenheit) and so it melts. But notice the temp drops down to 28 at the surface, so you get rain that freezes on contact, no bueno IMO.
The second has the same problem, but the are of above freezing is much small, so you get maybe a mix. Some snow flakes might survive, but those that melt re freeze as theyt fall through nearly 5000' of sub freezing air, so you get sleet.
Last one is the easiest. Starts as snow and never gets above freezing.
You may know some of this already, but wasn't sure based on your questions so apologies if it is too much. We want deeper cold so the snow doesn't have a chance to melt. The High being over the Great Lakes might help some as it would shift everything more east. But nothing is really showing anything like that for now, at least for the window I picked above. That high is sliding down the front range of the Canadian Rockies and will likely move in from the NW. Just a question of how far it makes it.