The answer to 'why is my shut-off valve frozen' is that the shut-off valve has likely become frozen due to exposure to cold temperatures. Shut-off valves are often located in uninsulated areas like crawl spaces, attics, or outside the home, which can cause them to freeze up during cold weather.
Common signs of a frozen shut-off valve include the valve handle being stuck or difficult to turn, no water flow when the valve is opened, and potentially water leaks around the valve. To fix a frozen shut-off valve, you'll need to thaw it out, which may require applying heat or insulating the area around the valve.