When it does thaw, it can create problems. Pilots fueling might not have found the contaminants right away, but eventually did. One pilot claimed an engine failure as a result. Doubtless you understand well that it's not a matter of if, but when the engine will fail. Every takeoff should be planned with the knowledge that the airplane may have to be put somewhere undesirable, and the takeoff made with that thought in mind.
Failures do occur.
Many are not so fortunate. Or to luck. If your instructors haven't done this, and haven't provided the information you should have, then it's a failing on their part in terms of proceedure, experience, and general knowledge. It's important not to be discouraged by this, but to seek out a qualified individual who can provide what is needed. 172's fly just fine in most all conditions and temperatures with common sense and a little care.