Mechanical is not feasible on the Mutt. You can put an electric one, but a 2 ton is not going to do anything to a stuck mutt.
When stuck multiply the weight by 1.5 & if stuck in snow, sand or muddy slush apply a 2.5 rate as the suction is greater. You probably need a 6000 - 9000 pound winch and a used one would cost around 12k. A new one, well sky is the limit.