With sleeve turned inside out, sew one end closed. Turn right side out. Push the balls, from largest to smallest, through the opening and to the bottom of the sleeve.
Tie thread between the balls. Sew the opening closed at the top of the snowman. Cut off excess sleeve above snowman. Wrap a 36-inch piece of wire around three fingers four times to make the hat brim. Switch to two fingers and continue wrapping to make the crown. At the brim, straighten the wire end and hot-glue in place to the snowman's head.
Fold an 18-inch length of wire in half. Make a small loop at the folded end for a hand. Twist the two wires together for 1 inch, then using one piece of wire, make a second loop and twist wires together for 1 inch. Continue twisting wires to 3 inches; repeat for other arm. Hot-glue arms in place on the snowman.
Loosely tie the linen strip around the snowman's neck. Hot-glue black beads to the snowman for eyes, and sew buttons to the body front.