I have taken fresh eggs.  Just crack them and mix them up and put them in a freezer bag.  I found that a freezer bag filled so the eggs are about 1/4" thick is very good.  This helps in thawing.  
When you go to make the eggs, put them in warm water, do not cook them just thaw them.  Having the eggs thin helps speed the process.  Then cook scrambled eggs as normal.  Sorry, overeasy never worked for us.  
Many other foods are not harmed in freezing, it is the thawing out for consumption that is the trick.  Some you can cook from a frozen state and some need to be genetly thawed, then cooked.
Winter camping is great fun if you are prepared for it.