Trickling water to keep the water lines from freezing is asking for disaster. You may keep the water lines from freezing, but now that water runs very slowly through your 3" waste hose where it can freeze easily. Then you have a 3" poopsickle, that backs up into, fills your grey tank and floods the camper while you sleep.
Do Not trickle unless you also have a heated insulated waste hose.
Even then there is the issue of wasting so much water for so little gain, when proaction will negate all issues.
Ask the camp hosts about what they do. They may shut the water off on cold nights,