Tyres will have far more effect than gizmos.
A tyre full of mud has no grip, spinning the wheel may throw some of it out of the tread but if it's not self clearing it's not gripping.
Road tyres, All terrain tyres and Mud terrain tyres all have differing grip characteristics in mud and no matter what the tyre once the grip is gone you are not moving.
Things like traction control can help , but traction controll and blocked road tyres still mean you are stuck, and not all tyres are equal even of the same type.
I have found BF Goodrich ATs far better than Cooper ATs for grip in mud as they clear better.
Whatever tyres are fitted momentum plays a big part in how far you get.
Paul.
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