Thoroughly combine the cream cheese, Worcestershire, lemon zest, 3 cups Cheddar and 1 teaspoon salt in the bowl of a stand mixer fitted with the paddle attachment, scraping down the sides with a rubber spatula as needed. Transfer to a bowl, then cover with plastic wrap and chill in the refrigerator until firm, about 30 minutes.
Roll the cheese mixture into three balls to form the base, body and head of the snowman. (They should be just over 4-, 3-, and 2-inches in diameter.) Roll the balls in the remaining 2 cups Cheddar to create a snowy exterior. Insert a 6- to 8-inch wooden skewer vertically into the largest ball; use it to attach the body and then the head of the snowman.
Cut an inch off the tapered tip of the carrot and use it for the snowman's nose. Insert the asparagus spears into the body for arms. Use two olive halves for eyes, and the remaining four for buttons. Wrap the thinly shaved cucumber or celery around his neck to form a scarf.
Serve the snowman on a platter surrounded by crackers.
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