Dude, Mercedes has plenty of experience and know how on 4wd systems You got UNImog built buy them even though a east European design bought and you have the G Wagon.
I have lived in snow and sand to know when a vehicle can and cannot be towed out follow the link below both diesel engine and do not have chains either just raised front bumper and ride height
YouTube - land cruiser wicklow snow wicklow mts
That bloody S-class has street tyres chains just gave it a bit more traction. That car could have easily come out with just a little tow pull properly done with any stock SUV with a bit of 4WD system, Yes I said Stock.
I was stuck in a similar snow situation in a Honda Accord in Northern Maryland and with push here and there the car made it out and it was stock!