Heat oven to 225°F and line 2 large baking sheets with parchment paper.

Using an electric mixer with the whisk attachment, beat the egg whites and salt in a large bowl on medium-high speed until stiff peaks form, 5 to 7 minutes.

Add the cream of tartar, then increase the speed to high and gradually add the sugar 1 Tbsp at a time, waiting 4 to 5 seconds between additions, until the meringue forms stiff glossy peaks; transfer ? cup of the plain meringue to a small piping bag with a small round tip. With the mixer running, add the food color to the remaining meringue and tint to desired color.

Transfer the red mixture to a large piping bag with a large star tip. Pipe Santa hats onto the prepared baking sheets, spacing them 1 ½ in. apart. Using the reserved plain meringue, top each peak with a dot (for the cotton ball). Bake, rotating the pans halfway through, until no longer tacky but still soft, 60 to 65 minutes. Let cool completely on the sheet.

Once cool, melt the white chocolate in the microwave. Dip the bottom ½ in. of each Santa hat into the melted chocolate, shaking off any excess, then immediately coat in the coconut. Repeat with the cotton ball. Transfer back to the parchment-lined baking sheets and let set.