Preheat oven to 400°. Line baking sheets with parchment paper.
In the bowl of a stand mixer fitted with the paddle attachment, beat butter, 1¼ cups granulated sugar, and brown sugar at medium speed until fluffy, 3 to 4 minutes, stopping to scrape sides of bowl. Add egg, beating well after addition. Beat in vanilla.
In a medium bowl, whisk together flour, cream of tartar, baking soda, and salt. With mixer on low speed, gradually add flour mixture to butter mixture alternating with Eggnog, beating just until combined.
In another medium bowl, stir together cinnamon, nutmeg, and remaining ½ cup granulated sugar.
Using a 1½-tablespoon spring-loaded scoop, scoop dough, and roll into smooth 1½-inch balls. Toss in cinnamon-sugar mixture until well coated. Place 2 inches apart on prepared pans.
Bake, one batch at a time, until edges are lightly golden brown but centers still look slightly wet, 8 to 10 minutes. Let cool on pan for 5 minutes. Remove from pan, and let cool completely on wire racks.
Recipe by Taste of the South at https://tasteofthesouthmagazine.com/eggnog-snickerdoodles/