Save yourself some time and mix everything the night before. Wake up with the sun and have this ready by the time the rest of your camp rises for the day.
Line a 9-inch springform pan with heavy-duty aluminum foil, lining all the way to the top edge of the pan. Lightly grease bottom and sides of foil with cooking spray.
Whisk together the cream cheese and maple syrup in a large bowl until combined; whisk in the vanilla, cinnamon, salt, and nutmeg. Whisk in eggs until combined; whisk in the milk. Add the bread cubes; stir to coat. Stir in apple and pecans, and let stand at least 30 minutes.
Heat a camping stove to medium-low (about 300° to 325°F), or fit a grilling grate over the direct heat of partially glowing embers. Cut 6 (18-inch) squares of foil; crumple each foil square into a 1 1/2- to 2-inch ball. Arrange the foil balls on bottom of a 7 1/2-quart cast-iron Dutch oven; cover with lid. Preheat on the camping stove or a grilling grate directly over the heat source 10 minutes.
Pour the bread cube mixture into the prepared springform pan. Place the springform pan on top of the foil balls in the preheated Dutch oven. Coat a large sheet of foil with cooking spray, and place over the top of the Dutch oven, coated side down. Press the foil around the top edge to tightly seal, and cover with the lid. Bake until a knife inserted into the center comes out clean, about 2 hours. Let stand 10 minutes. Remove the sides of the pan; remove the foil from the sides of the strata. Cut into wedges; lightly sprinkle with powdered sugar, and serve with maple syrup.