Refugees on the path
If you are a refugee yourself, you have to weigh traveling in the pack. This will be what it essentially will become. The pack travels together for protection. Of course it is better to travel with people you trust, but it may be quite random based upon when you leave, when you run out of gas, when you get stranded, run out of food, etc.
You have to weight how trustworthy are each and every person in that group, and if traveling in that group benefits you and your family more than traveling alone. A pack when hungry can go feral.
The pack may travel directly down previously detailed paths following the strategies I've described. Those paths may not make the best sense since what few resources found may have to be divvied up among pack members. You could find yourself in a situation of trouble caused by the pack, or attributed to their presence. Personally I would never travel in a pack of random strangers.
I think that traveling on open roads is highly dangerous. Towns not wanting strangers will reject refugees. Some refugees may set up where they can. They may decide that living under a bridge intersecting a highway is a good place for them, and they may in fact prey on other refugees.
If you know the North well, even though it is cold, places like upper state Maine, that have extremely low population density, high availability of natural resources, abundant game, etc may be far better than doing whatever is the current paradigm for refugees. Any diversions to Northern climes will mean knowing survival techniques completely based upon weather patterns.
There are many places in the USA that are off the beaten path, and have similar characteristics to the above, but are warmer. Some are populated with rednecks. I am a redneck myself. You can do well in the woods, but it would require a radical lifestyle change. You would definitely be a lot skinnier. Holing up in a place with minimal people, and staying there until things settle down, and out of sight of strangers, might be a very good strategy. Did I mention that those places are populated with rednecks though? That alone will preclude people from living in those locations. :) Rednecks can be the most hospitable people or the least hospitable people, and much of it is based upon your own attitude.
At some point, anyone who bugs out, and lives alone in the woods, will come out for information. Since the last refugees are treated with hostility, dropping in to a town will be risky at a late point. All of us are judged in the first three minutes of contact with another person, and that is based upon a social transaction under the best of circumstances.
Realistically speaking, even if you had a month of supplies, great survival training, and were a perfect trapper, the most you could hold out is two months. The reasons is simple. We are social creatures. The worst sentence in prison is solitary. Very few of us are wired to be alone. If you are a family of four, you might hold out two months in the woods, if perfectly supplied and full of survival skills. Having the support of family is so vital, you might be surprised. Most people won't last three days in the woods if alone, without food, and not having skills. People who can adjust, find water, do a mind-shift and eat things they thought they couldn't, can last a week if they find shelter. The simplest accident can kill you in the woods if you don't know anything. It can happen in hours after becoming lost.