This is the simplest and most common way to spike hot chocolate; all you need to do is add a little peppermint schnapps to the cocoa. Not only does this create a hint of alcoholic warmth, but the peppermint taste of the schnapps brings some depth to the flavor, making it just a touch sweeter.
One garnish I find almost essential for this drink around the holidays is mini candy canes. Just hang one on the side of the glass and allow it to melt in the warmth for an even mintier touch.
According to "The Bartender's Black Book," you may also hear this drink referred to as a Peppermint Kiss, Cocoanapps or Snuggler.