The answer to 'why is my shut-off valve frozen' is that the shut-off valve has likely become frozen due to cold temperatures. Shut-off valves are often located in unheated areas like basements, crawl spaces, or outdoors, making them susceptible to freezing when the temperature drops.
Some common causes of a frozen shut-off valve include a lack of insulation around the valve, prolonged exposure to cold air, and water that has seeped into the valve mechanism and then frozen. This can prevent the valve from opening and closing properly, which can lead to further problems if the pipe bursts.