I'm kinda guessing, but I get the impression the hose is there to direct any water pump leakage safely to below the engine. It's probably a worn out water pump that needs to be replaced.

If you still need further verification whether it's coming from inside the hose or dripping on the outside, pack some absorbent material around the outside of the hose to stop any drippage and see if it still leaks from the hose end.

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95 E320 Cabriolet, 169K