The 2006 Mini Cooper S has something call DTS (Dynamic Traction Control). If one of the two front tires is on dry pavement and one of the tires is on ice, The cars Dynamic Traction control system will not let you just “Spin the tires” effectively.
I would still use lots of salt around the tire, I would also press and hold the DSC button. This turns off the DSC (Dynamic Steering Control), and DTS systems.