Melt white chocolate chips and coconut oil together until smooth.
Dip the flat side of one Oreo in white chocolate and stack a second Oreo on top; repeat to make a 3-Oreo snowman stack. Set on parchment.
Let stacks set for 10 minutes in the refrigerator.
Dip the entire snowman stack in white chocolate or drizzle white chocolate over each stack to coat.
While chocolate is still wet, add mini M&M buttons and press in pretzel stick arms.
Once chocolate is set, use icing pens to draw eyes, a carrot nose, and a smile on the top Oreo.
Let dry completely before stacking in a gift box.