With the rack in the center, heat the oven to 350°. Line two baking sheets with parchment paper. In a medium bowl, whisk the eggs until they're frothy, about 1 minute. With a wooden spoon, stir in the condensed milk, corn syrup, salt, and vanilla extract until blended. Stir in all the coconut until evenly mixed.
With wet hands, roll heaping tablespoons of the coconut mixture into balls, pressing them tightly together. Place them on the baking sheets, 1 1/2 inches apart. Shape each ball into a cone.
Bake the macaroons until their edges are golden brown, about 15 minutes. (Take care not to overbake them, or they'll be too hard when cooled.) Set the baking sheets on a wire rack for a few minutes, then transfer the cookies to the rack to cool completely.
Place the white chocolate in a medium, heat-proof bowl, then set the bowl over a pan of simmering water. Do not let the bottom of the bowl touch the water. Let the chocolate melt, stirring occasionally, until smooth. Remove the pan from the heat and add the vegetable oil.
Hold a macaroon by its bottom edge, dip it in the chocolate, and gently shake off the excess. With your other hand, use a spoon to sprinkle the top three quarters of the macaroon with red sugar until coated. Sit the macaroon flat on one hand, and with the other, carefully press finely shredded coconut onto the bottom quarter of the hat, turning the macaroon as needed. Return it to the wire rack to let the chocolate set for a few minutes. For the pom-pom, place a mini marshmallow on the end of a toothpick, dip it in the melted chocolate, let the excess drip off, then roll it in finely shredded coconut. Dab a small amount of white chocolate on the pom-pom and adhere it to the top of the hat.
Repeat step 5 with the remaining macaroons. Let the chocolate set completely before storing the cookies in an airtight container.