Whisk the milk, granulated sugar, and horchata mix together until all is dissolved. Stir in the heavy cream and vanilla extract.
Turn on your ice cream maker and pour the mixture in. Once the ice cream is pretty well set up (near the end of the cycle) sprinkle in the cinnamon.
Once the ice cream maker is finished, allow the ice cream to continue hardening in the freezer for a couple hours, or eat soft serve as is.