It’s more because of the temperature differential. The more difference between the temperature of two objects, the faster they change temperature. A radiator with 50 degree water is ~30 degrees warmer than the room (or 80+ degrees for a steam rad), while cold water is going to be 10-15 degrees cooler than the room. Any colder and you need to use not-water so it doesn’t freeze. Condensation or frost is also a big concern to avoid property damage.