Freezing teethers can cause the teether to become very hard, meaning it would cause discomfort and possible injury to a baby's gums when trying to chew on it. Depending on how cold the teether gets, it could also cause frostbite on the baby's gums.
A person should refrigerate a teether briefly to keep it cool. Testing it in another person's skin before passing to a baby may help determine if it is within a safe temperature range.