Use a concentrated red food coloring gel (not liquid food coloring) for the brightest results. When baking the meringues, don't open the oven after turning it off; this will help them dry.
Preheat oven to 225°F. Line 2 rimmed baking sheets with parchment paper.
Place egg whites in a clean, dry bowl. Beat with an electric mixer on medium-high speed until foamy. Add food coloring gel and cream of tartar. Increase speed to high, and beat until mixture forms soft peaks. Gradually add granulated sugar, beating until whites are stiff and shiny.
Sift together powdered sugar and cocoa in a separate bowl. Sprinkle one-third of powdered sugar mixture on egg white mixture; gently fold until thoroughly incorporated. Repeat procedure 2 times with remaining powdered sugar mixture. Transfer mixture to a large piping bag or large ziplock plastic freezer bag with 1 corner cut about 1/2 inch to form a piping tip.
Pipe meringues onto prepared baking sheets, forming small “Santa hats” by piping a 1 1/2-inch-wide round and swirling and lifting up bag. Bake in preheated oven until meringues are firm and dry, about 1 hour and 30 minutes. Turn off oven, and let meringues stand in oven with door closed 20 minutes.
Remove meringues from oven, and cool completely on baking sheets on wire racks, about 20 minutes. Gently peel meringues off parchment.
Place chopped white chocolate in a small microwavable bowl. Microwave on MEDIUM until melted and smooth, about 1 minute and 30 seconds, stirring every 30 seconds.
Place edible candy paper shreds in a shallow plate or bowl. Dip bottoms of meringues in melted white chocolate, and dip in edible candy paper shreds. Place on parchment paper, and let stand until set, about 30 minutes. Dip cut halves of marshmallows in melted white chocolate, and place on tips of Santa hats. Let stand until set, about 15 minutes. Store in an airtight container at room temperature.