When you are making coffee with a coffee maker, you are in control of the temperature. They are designed to contain the heat, but they do not create it. You are responsible for heating up the water and brewing the coffee. This means that you can make cold brew coffee with them. Honestly, the process is probably easier than you think. Although, it will take several hours to achieve. Note, this is not intended for stovetop versions.
To start, place your coffee grinds (after you have grounded them up) inside the machine. Then, add the appropriate amount of water but only make it room-temperature (as opposed to 205 degrees Fahrenheit). Proceed to mix the grinds into the water and then, it is time for you to wait several hours. For around 12 hours, place the coffee maker in your fridge. Once it has been refrigerated for this amount of time, make the coffee as you normally would be pressing down on the plunger.
Now, if you want to have this for your camping trip and do not have a way to refrigerate it, make it beforehand and store it in your cooler.