Springbok, over here we very much require additives during the winter months especially so. If plain water is kept in the reservoir/supply tank, algae can form, presenting a real problem. I had an example of this a couple of years back so decided to try to clean out the system. It took ages to clear the foul stuff out of the tank, which was the main fault I reckon, i.e. additive had not been used?
After the tank had been cleaned, blow the lines through with compressed air, after disconnecting the nozzle jets, then follow on by disconnecting the jets themselves, and cleaning them out,a fine wire bristle pulled from a wire brush is great, as pins and soforth are often too thick? Sorted!
As was mentioned, cut the pipe if needs be, as new washer hose is cheap and available, as are the barbed plastic connectors, should you require them. Sometimes the small rubber impeller vanes in the pump itself can become worn out too, as well as the motor itself, but normally only after years of use.