What could cause my water heater to pulsate during cold water usage?
Sounds like the pressure regulator is failing and needs to be replaced. Last time mine went, it would bang all the pipes after I used any water, hot or cold. Depending on your existing pressure regulator and the replacement you find, it may be as easy as unscrewing the old one and screwing on a new one. But more than likely, you'll need to cut the pipe and solder (assuming copper) a new connection or two.