Here's some diagrams that might help you understand what's in your car:
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Look at the diagram at the bottom center of the page and note the unlabeled device at the top of the picture... that's a metal diverter valve that sits in the engine compartment and has heater hoses connected to it. The heater hoses are attached to the nipples shown at the top and right coming out of that valve, the small hose shown as white in the diagram is a vacuum hose that actuates the diverter valve to send hot water through to the heater core under the dash when you turn on the heater, or to bypass the heater core and send the hot water back to the engine.
note: This particular picture shows a system without a/c, but I believe that same valve is present on cars that DO have a/c as well, but they just don't show it on the a/c diagram (upper left on the page), they only show the airflow door actuators. I don't have a C3, so I can't verify that.
That valve can stick or become disconnected from the vacuum hose, or there could be a leak in the vacuum system that prevents sufficient vacuum from reaching the valve. It is a common point of failure. The valve is not particularly expensive to replace.
It could be checked by applying vacuum directly to the valve to see if the heater then works (you should be able to feel that the water hose from the diverter to the heater is cool before vacuum is applied, then heats up with vacuum applied). You may need a vacuum pump to test with, or you can "borrow" vacuum from another vacuum source on the engine by "Tee"ing into that good vacuum source. (Simply sucking on the hose orally is not likely to produce sufficient vacuum.)
You could also disconnect the two water hoses from the diverter valve and clamp them to opposite ends of one short section of copper tubing (5/8" I believe) to bypass the valve for the winter, then reattach them to the diverter valve in the spring.
Good luck.