The reason your current code isn't working is that calling Thread.Sleep() stops any execution on the current thread until the time given has elapsed. So if you call Countdown.Start() on your main game thread (which I guess you are doing), your game will freeze until the Sleep() call has finished.
Instead, you'll want to use System.Timers.Timer
Take a look at the MSDN documentation.
UPDATE: Now hopefully matches more your scenario
public class Timer1
 {
     private int timeRemaining;
     public static void Main()
     {
         timeRemaining = 120; // Give the player 120 seconds
         System.Timers.Timer aTimer = new System.Timers.Timer();
         // Method which will be called once the timer has elapsed
         aTimer.Elapsed + =new ElapsedEventHandler(OnTimedEvent);
         // Set the Interval to 3 seconds.
         aTimer.Interval = 3000;
         // Tell the timer to auto-repeat each 3 seconds
         aTimer.AutoReset = true;
         // Start the timer counting down
         aTimer.Enabled = true;
         // This will get called immediately (before the timer has counted down)
         Game.StartPlaying();
     }
     // Specify what you want to happen when the Elapsed event is raised.
     private static void OnTimedEvent(object source, ElapsedEventArgs e)
     {
         // Timer has finished!
         timeRemaining -= 3; // Take 3 seconds off the time remaining
         // Tell the player how much time they've got left
         UpdateGameWithTimeLeft(timeRemaining);
     }
 }