Chop broccoli into bite-sized pieces. Slice olives; cut carrots and bell pepper into small pieces. Separate bagels into halves.
Spread cream cheese onto the bagel halves.
Curve a green onion around the top of each bagel half; add broccoli to each end for the ear muffs. Add olives for eyes and carrot and bell pepper pieces for the nose and mouth.
Serve snowmen with apple slices and any remaining ingredients on the side.