To make the cookies: Place the margarine and sugar in the bowl of a mixer fitted with a paddle and mix until smooth. Scrape down the sides of the bowl and add the eggs, one at a time, beating well and scraping down the sides of the bowl before each addition. Add the flour, cream of tartar, baking soda, and salt and mix until everything is well incorporated. Cover with waxed paper or plastic wrap and refrigerate at least 2 hours or freeze up to 2 weeks.
To make the cinnamon sugar: Place the sugar and cinnamon in a small bowl and mix to combine.
Preheat the oven to 400 degrees.
To form the cookies, break off small pieces and roll into 1-inch balls. Roll the balls in the cinnamon sugar and place on an ungreased cookie sheet.
Transfer to the oven and bake until just barely golden, about 8 to 10 minutes. For crisper cookies, cool on the cookie sheet. For softer cookies, cool for 2 minutes and then remove to a rack. Cool the cookie sheet between batches.
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