Continuity mistake: After Jack dies his son is making a snowman that later becomes his dad . You briefly see a scarf around the snowman. A little after that he puts the same scarf on the snowman.

Jack Frost (1998)
1 review
Directed by: Troy Miller
Starring: Michael Keaton, Kelly Preston, Mark Addy, Joseph Cross
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Despite some good performances from Michael Keaton (when he is a human), Kelly Preston and the actor playing the boy, Jack Frost is ultimately weighed down by an overly schmaltzy tone and the design of the snowman is far too distracting to be considered heartwarming.
Charlie: You the man.
Jack: No, I'm the snowman.
Trivia: You may notice that the snowman looks a little familiar, but doesn't quite look like Michael Keaton. This is because originally, George Clooney was supposed to star in the film, and the snowman was designed to look subtly like him. Clooney dropped out at the last minute and was replaced by Keaton, and the effects teams didn't have quite enough time to totally redesign the snowman. (They only had time to make a few minor tweaks, like his eyebrows).
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Answer: Wire Fox Terrier.
Bishop73