Cross country road trip in November/ December with a child... what states should we avoid?

We are planning on renting a car and road tripping with our one year old for six weeks. Previously, we did similar trips in July/ Aug and Oct/ Nov in the past, and we were able to go pretty much anywhere without issues. Additionally, we're not necessarily asking about places we should "avoid" but more what states are a "no go" if we were to encounter blizzard conditions. That being said, we've ruled out Minnesota, Wisconsin, Michigan, New York, Pennsylvania, Massachusetts, Vermont, New Hampshire, and Maine. Not only does it snow a lot in these states, but it also gets very cold. I'm wondering what other states should be ruled out. For example, I've heard that Ohio and Indiana don't get a lot of snow, but that it can dump on them unexpectedly at times. Places like Arizona, Nevada, Utah, Colorado, and New Mexico seem like a safe bet. Texas might be okay, but not if we plan on going into the panhandle. The Dakotas seem like a no go as well... as well as DC, New Jersey, Delaware, Maryland, Kentucky, West Virginia, and Virginia. We're looking to start from Atlanta, and want to go to the Grand Canyon. If we leave out the "no go" states, it seems like we'll have to go through Tennessee, Arkansas, and Oklahoma to get there. On the way back, we could go through Louisiana, Mississippi, and Alabama. We've already traveled through Georgia and the Carolinas. Is our map correct?