These are strawmen arguments. Nobody has said that you can't have a winter storm without a high. And nobody is saying that you always have to have a high to get a winter storm. But for non-climo areas, a high pressure in or near a favorable spot is more ideal than the reverse, if you are looking for a widespread winter storm. Northern and northwestern parts of the SE have a much easier time seeing snow in marginal setups where there is no strong cold air feed.Bingo. Yes it's really not that simple as some here are trying to make everyone believe. It's not as easy as give me cold air & a big cold high to the north to transport and then that's automatically the best setup for everyone. It gives you a certain type of winter storm but that's not always a good setup for most including areas like say the coastal plain/I-95 corridor of NC, where Miller A cyclones usually deliver bigger winter storms per capita than overrunning or CAD.
Stable cold air transport into the area widens the window for frozen precipitation for a greater duration of the storm. It's not a guarantee, but it is generally a better scenario than having a stale air mass in place or hoping that a wave sneaks in before the fresh air mass quickly departs.