Place the Dutch oven on a hot campfire grate. Add sauerkraut and beer to the Dutch oven. Nestle the hot dogs into the sauerkraut and close the lid. (If there's not enough liquid to cover the hot dogs, add 1 cup water.)It's fine to leave the hot dogs in the sauerkraut for a few minutes until everyone is ready to eat. The timing for this meal is quite flexible. That said, if the hot dogs begin to burst on the ends, it's time to take them out of the sauerkraut!
Place a cast-iron skillet on the campfire grate until the skillet is hot. Use tongs to move a few hot dogs from the sauerkraut to the pan. Rotate the hot dogs occasionally until they're evenly charred, and then remove from heat.If your campfire grate is too small to fit both the Dutch oven and the skillet, you can remove the Dutch oven from the heat at this point.While the hot dogs cook in the pan, place the hot dog buns on the campfire grate over indirect heat. Allow the buns to toast, turning occasionally. Once toasted, remove the buns from the heat and replace with remaining buns.
Serve the hot dogs and sauerkraut in the buns and top with mustard.