Frictionless Ice.
Give the player an X and Y velocity, which then is added onto the X and Y coordinates every loop. When you stop moving, rather than immediately setting the velocity to 0, have it subtracted by a "friction" variable every loop until it's 0. So when you let go of the control stick, you won't immediately stop in place, but will slide a bit. Turn the friction down to slide further, turn it off and you will slide forever.