Heat oven to 350°F. Line baking sheets with foil; coat heavily with nonstick cooking spray. Mix condensed milk, vanilla, and salt. Stir in coconut until well blended.
Drop scant measuring tablespoonfuls of dough in 1-1/4-inch mounds on sheets spaced 2 inches apart. Place a cherry half on lower part of each mound.
Bake one sheet at a time, in upper third of oven, 18 to 20 minutes, or until lightly browned. Transfer sheet to wire rack and let stand until cookies are thoroughly cooled. Carefully peel cookies from foil. Add currant eyes above cherries. Break pretzels to resemble antlers and poke into tops of cookies.