In a large skillet over medium heat, brown the sausage, stirring frequently, until cooked through, about 6 minutes. Use a slotted spoon to transfer the sausage to a bowl, leaving the fat in the skillet.
Add the hash browns to the fat in the skillet and cook over medium heat, stirring frequently, until golden, 5 to 6 minutes. Season with the salt and set aside.
Whisk the eggs in a large bowl, then pour them into a medium non-stick skillet. Cook, stirring frequently, pushing the cooked curds to the center of the skillet and allowing the uncooked egg to fill in the space behind until all of the egg has formed soft, creamy curds, about 5 minutes. Remove from the heat and set aside.
When the sausage, potatoes, and egg have cooled to room temperature, assemble the burritos by topping each tortilla with ½ cup sausage, ⅓ cup hash browns, ¼ cup cheese, and 3 tablespoons scrambled egg.
Roll each burrito up by folding in the sides and then firmly rolling from one edge, keeping the sides tucked in. Wrap each burrito in foil, and label if necessary. Refrigerate or freeze until you're ready to cook.
To heat the burritos, set them on a campfire grate over hot coals, or on a portable grill over low flame, or in a skillet on a camp stove over medium heat. Cook until the filling is heated through and the cheese is melted, about 20 minutes for thawed burritos. Frozen burritos will require an additional 5 to 10 minutes.
Serve with hot sauce or salsa, if desired.