Let cream cheese and sharp cheddar come to room temperature. In the bowl of a stand mixer fitted with a paddle attachment, combine cream cheese, cheddar cheese and ranch dressing mix.
Divide cheese mixture and form one smaller cheese ball for the head and one larger cheese ball for the body. Transfer cheese mixtures to two separate sheets of plastic wrap. Refrigerate for at least 4 hours, or overnight. Can be made several days ahead.
Right before serving, press shredded cheese into cheese ball. Place on a serving plate and place smaller cheese ball onto larger cheese ball. Slice the tip off of a baby carrot and press into cheese ball to make a nose. Use whole peppercorns for mouth, eyes and buttons. Serve with crackers.
Cheese Ball can be mixed and refrigerated up to three days before. Add jack cheese and snowman decorations right before serving.