Summer tires on wet grass are horrible, if you want to be driving the Z in the winter time you really need a good set of snow tires.
Were you able to get the car unstuck? Despite what the manual says I would consider using the rear hook in certain cases, to carefully winch across flat ground or a very light slope perhaps. In these cases you are only exerting maybe 200 lbs of pressure. Using it to pull up a steep hill or winch onto a flat bed would be a no.
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