In the winter in snow country, we take a dozen fresh eggs to the trailhead, then crack them into a Nalgene water bottle. They carry easily that way, and they don't seem to spoil in cool air temperatures.
In the summer, that would get tricky. You never know when you will get a hot day that could cause all sorts of things to grow. As a result, powdered eggs are much safer. Now, if you are not used to powdered eggs, you may not like the texture. However, I spent one entire winter in the military eating powdered eggs, so I got used to them. Here is the trick. You have to add some oil into the mix, not just water alone. You can use olive oil, vegetable oil, meat grease, butter, margarine, or just about anything, and it doesn't have to be much. Try the equivalent of a quarter of a teaspoon of any oil to each powdered egg equivalent. Then fry it as you would a normal fresh egg. The Army cooks used to whip the egg mixture before frying or cooking, and that worked best.