Preheat oven to 350 degrees F.
Lightly spray a 6-cavity donut pan with cooking spray and set aside.
In a large mixing bowl, whisk together the flour, sugar, baking powder, baking soda, salt, cinnamon and nutmeg.
In a large measuring cup, whisk together the apple cider, coconut milk, applesauce, and apple cider vinegar.
Pour the wet ingredients into the dry and mix until just combined. The batter might seem a bit wet, but don't worry - this is going to keep the donuts soft and moist.
Pipe the mixture into the prepared donut pan using a pastry bag (or just use a spoon). Fill each cavity just to the top, but don't overfill.
Bake the donuts for 11 to 13 minutes until the donuts are firm. The batter will have pulled away from the sides of the pan and when gently pressed will "bounce" back.
While the donuts are baking, mix together the sugar and cinnamon for the topping and set aside.
When the donuts are done, let them cool in the pan on a wire rack for just about a minute or two - until you can handle them without burning yourself. They should slide easily out of the pan. Immediately dip each one into the cinnamon sugar mixture while they are still quite warm and return to the wire rack to continue cooling.
These delicious donuts are best served warm. Try not to eat them all in one sitting. I dare you. :)