Yes rivers freeze but only on top. There is still flowing water under the ice. Dad owned a car wash all we did in the winter was open a valve and let a small amount of water pass through the spray wands onto the ground. Even in 20 degree temps the running water keep the lines from totally freezing. When the valve was totally opened and let more water flow the increased water flow will get rid of any icy mixture that is in the hose. To relate this to a camper I would install a Y fitting at the rv connection point and let a small amount of water piss out. This will keep the water hose from freezing if you have a sudden cold snap. If you are a frequent cold weather camper then you should invest in a heat trace water hose.
Also, ALL the water coming down the river is close to 32 degrees, where as the water in the car wash is coming from a pipe buried below the frost line and is probably running about 55 degrees or so, so it doesn't freeze because it doesn't really have enough time to get cold before it's out of the pipe and onto the ground.
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