Does your trailer have a bypass valve setup for bypassing the water heater when you winterize the plumbing?
It doesn't sound like hot water is getting into the freshwater tank, it sounds like it's being distributed to the cold-water lines by some cross connection. The most likely thing I can think of are water-heater bypass valves that are halfway between bypassed and on, especially if this hasn't happened before.
Il Carriaggio — 1975 Argosy 24 | Il Progetto — 1976 Argosy 28 Center Bath | WBCCI# 15566
He has all of the virtues I dislike and none of the vices I admire. — Sir Winston Churchill