Certainly at some schools, pressure is put on Flight Instructors to get in the air early. This can sometimes mean going up in weather that isn't 100% suitable for the lesson, or pushing the boundries a bit more by flying with ice on the wings.
Deicing fluid is expensive, and is often overused (quite rightly) by people being over cautious, rather than used sparingly. From the point of view of the CFI/school owner, this is wated money, and even more wasted by the aircraft being on the ground being deiced.