Whereas winter weather can cause disruptuions and you should allow extra time for your journey 'just in case', you have to remember that the country doesn't shut down in the winter and that Interstates are the top priority to keep open and everyone on the move, so no, winter driving does not equal certain death and you can't drive across the country without tackling mountain passes. It should also be noted that Interstates are designed with gradual curves and gradients for ease of driving for the biggest of rigs.

Now about the time factor, you haven't mentioned how long you have in total for the trip, but LA to Albu is more than a days drive as is the onward journey to Fort Smith and even Nashville to Washington is beyond what we would recommend, so I hope you are planning on breaking those legs of your trip up differently and they are not daily targets. You will not know what the weather will bring or what the road conditions are like until a couple of days before so it's important to keep up with to date with whats going on and plan from there. Snow chains are handy back up tools in a crisis but if it gets to the stage that you would need them then the safest thing to do is hold up somewhere until the storm passes and the road crews have done their job of making the Highways safe.