My family recipe for snickerdoodles calls for cream of tartar and I always thought that ingredient was an essential part of the "snickerdoodle...

Hilarybee, you should definitely post that recipe! Let me know if you do. I like the bit of an edge that cream of tartar lends to the mix. Ciao ciao

I recently tested a superb snickerdoodle recipe that does not contain cream of tartar. "Baker's Best Snickerdoodles" from the Rosie's Bakery All-Butter, Cream-Filled, Sugar Packed No Holds-Barred Baking Book.
It calls for quite a lot of baking powder 1 tablespoon plus 1 teaspoon of double acting baking powder for a batch of thirty cookies. The results were significantly better than my own recipe that uses Cream of Tartar.

Cream of tartar (tartaric acid) is also used as a bittering agent, so think about it and the flavor profile of snickerdoodles in that context.

Cream of tartar and baking soda in a 2:1 ratio is a formula for home made baking powder. A newer recipe is likely to use double acting baking powder. Ideas in Food, by Kamozawa and Talbot, has information on this on pages 97 and 98.
My mother made Snickerdoodles from the Betty Crocker Cookbook, 1950, and I see that's exactly what they use in the recipe.