In my opinion, LHP and RHP cannot be defined abstractly, in terms of just one aspect of the principles or aims of a particular path. Instead, I regard LHP and RHP as groupings that have evolved spontaneously, and whose meaning is mainly social and historical.
The cold plate causes the moisture in the warm air, which is inside the jar to condense and form water droplets. This is the same thing that happens in the atmosphere. Warm, moist air rises and meets colder air high in the atmosphere. The water vapor condenses and forms precipitation that falls to the ground.
Freezing rain occurs when rain forms in a relatively warm (above freezing) layer of air and falls through a shallow layer of air that is below freezing. The rain is supercooled (still liquid) as it falls through the cold layer near the surface of the earth.