According to the reputable explanatory dictionary by S. I. Ozhegov, a "tsutsik" is simply a puppy. The Russian Etymological Dictionary notes that the word originates from the sound "tsu-tsu," used to call dogs, similar to "tsip-tsip" for birds.
One theory suggests that the phrase "to freeze like a tsutsik" emerged from a mix of foreign words and Russian meanings. During Catherine II's reign, immigration to Russia was encouraged. In Bavarian and Austrian dialects, there’s a verb "zuzeln," meaning "to suck, lisp, or tug," which resembles the Russian word "tsutsik." Additionally, Germans have the expression "frieren wie ein junger Hund," which translates literally as "to freeze like a young dog (puppy)."
If we consider the level of hypothermia implied by comparing a person to a freezing puppy, it means rapid chilling accompanied by shivering, as newborn dogs lack thermoregulation.