Seperate dough into strips. Wrap one strip of dough around each hot dog, leaving 1/2 inch uncovered for face. Arrange on a lightly greased baking sheet.
Whisk together egg and water; brush over dough. Bake at 350° for 14 to 16 minutes, or until golden. Dot mustard on hot dogs with a toothpick to form eyes, if desired.