Answer
No, there is no such thing as "cold flow".
Work Step by Step
Heat transfers from higher temperatures to lower temperatures, from your hot hand to the cold ice. The energy leaving your hand gives you the feeling of coolness.
You can help us out by revising, improving and updating this answer.
Update this answerAfter you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.