Cut out the base strip for each hat. Cut construction paper into 4-by-11-inch strips. Orient the paper horizontally to use the widest area of the paper. Choose construction paper in colors matching the animals being created. For example, pink paper works for a pig, yellow for a duck, white for a rabbit and gray for a mouse.
Loop the strip of paper to form a circle and secure with staples, glue or tape. Allow preschoolers to help with the process by using glue sticks which are easy for small hands to maneuver.
Cut out ears for each hat in matching colors of constructions paper. Create rabbit ears by cutting out two long white pointed ovals and two smaller pink ovals. Attach the pink on top of the white. Craft reindeer antlers by tracing around a preschooler's hand on brown construction paper and cut out the shape. Additional ear options include half circles in gray for a mouse, triangles in black for a cat and pink circles for a pig. Tape, glue or staple the ears to the back of the paper circle hat.
Place the paper animal hat, with the ears oriented to the back, and add eyes to the hat. Use a black marker to draw eyes on the front of the hat. Leave room in the center of the hat to add a hand-drawn nose for animals with distinctive noses. For example, a black circle with two dots in the center works for a pig snout and a black triangle with lines for whiskers works for a cat.