Preheat the oven to 350 degrees Fahrenheit.
Mix the ingredients for rolling the cookies -- the cinnamon and sugar -- in a small bowl and set aside.
In a bowl, whisk together the dry ingredients: the flour, cream of tartar, baking soda and salt. Set aside.
In a large bowl or the bowl of a stand mixer, whisk together the butter and sugar (use the paddle attachment on your stand mixer) until fluffy, about 2 minutes.
Add the applesauce, apple cider vinegar and vanilla, scrape down the sides and bottom of the bowl, and mix.
Add the flour in two batches until combined. You can do this with the paddle attachment, beating for only 20 seconds after each addition and then continuing to mix with a spatula. The cookie batter might look a bit dry but it should easily hold together when you form a ball with your fingers.
Shape the cookie dough into balls slightly larger than an inch, roll them generously in the cinnamon sugar, and place them at least an inch apart on an ungreased cookie sheet.
Bake in batches for 11 minutes. Remove the cookies from the oven, let the cookie sheet stand on a rack for about 10 minutes, then transfer the cookies directly to a rack to continue cooling. Your cookies might appear very soft but they will firm up a bit as they cool. If you bake for longer, your snickerdoodles will be crispy. Still very tasty and great for dunking though!