Stocking Cap and Ski Mask

If you're crossing over the mountains or find yourself deep in winter, a ski mask is a very handy item as it will help keep your head and face warm at night, when you sleep.
You should also have a stocking cap, which you can pull on over the top of the ski mask, and keep yourself even warmer thanks to the added layer.
Black Open Face Ski Mask with Brim - Dozen Packed(Case of 12)

Tipi Tent

If you have a large canvas tarp, or 3 or 4 small canvas tarps in your party, you can quickly assemble a tipi like the Native Americans of the Great Plains. If it's large enough, you can even have a small campfire inside.

Cut down a small number of slim trees, and trim off all branches, and then lean them up against each other, and then wrap the canvas around the structure, leaving a small hole at the top (so smoke from your campfire can escape). Be sure to wrap the canvas in a way that leaves you with a small door you can peal back to enter and exit, that points away from the wind. (If the tipi is big enough, four or five of you can all sleep inside by the fire.)
10' x 12' Heavyduty Tarp

Solo Tent

Preparation is key. It will be smart to sacrifice items that will weigh you down, such as a full size tent, and instead assemble a makeshift tent yourself out of heavy duty canvas tarp and duct tape -- or a "Solo Tent".

The Solo Tent will be your best friend when you have to travel cross country, because it's very light weight, takes up very little room in your backpack (you can roll it up and tie it to the outside of your pack), and sets up in less than a second.
It's also very cheap to make.

Cut a heavy duty canvas tarp into a 7 x 8 piece. Then fold it so that the opposing edges touch. Then run multiple layers of duct tape along the outside edges and inside edge, so there's a perfect seal that will hold up to heavy use, leaving one side open so you can enter and exit. You now have an instant shelter, that rolls up like a sleeping bag to take up very little space in your back pack. To use it, pull it out of your pack and unroll it. Next, unroll your sleeping bag, and place it in the Solo Tent, so that the Solo Tent fits like a sock over the sleeping bag. It may not seal at the end, where your head will be when you're laying down, but that's fine -- you need to breathe right?(Consider making two or three of these; especially if it's likely you'll be traveling with others).

Avoid all mushrooms. I've read that many can kill, while others will make people severely sick, and identification is sometimes misleading. All this considered, I think it's better to just treat all mushrooms as off limits.

Permanent Camp
After you've covered many miles, and you're a few days into your trek, choose a location for your camp that is near a water source, like a river, creek, or lake, and offers secrecy.
Anything flanked by mountains and surrounded by forests will help.
Burn your campfires at night, and burn them in such a way that those in the towns and cities can't see the light the fire gives off. For example, build your fire behind dense brush. Don't build your fire on a barren hill.
Use common sense, geared to the situation. Think things through, don't panic.
Survival is about using all your mental and physical skills.