I've caravanned for 28 years now and had to ask for a tow in January this year when we were surrounded by 7" of snow. Our friendly site warden Dennis, drove his trusty 1950's Fergie tractor without a cab over at towed us off. Even he had wheelspin so you can imagine how bad the weather was. I did tip him a drop of Scotlands finest to warm him up. That was my first time I'd needed a tow off.
I carry a hand winch, track mats and a tow rope as part of my normal kit, but trying to winch off in heavy snow is "snow joke"!!
One thing I've found quite effective is to lower thw tyre pressure of the drive axle tyres to 10Psi. This put's down a larger foot print of tyre onto the ground. Of coarse, one must have a pump handy to re-inflate the tyres as soon as you are on firm ground. Also do not travel more than walking pace as you do risk damaging the sidewalls of the tyre if you go faster. But when your stuck you do have to think outside the box.
By far the best and first coarse of action is to contact the site warden and ask for a tow. That way, if he refuses you can ligitimately use your recovery methods and should minor grass damage be caused, you can't be deemed irrespossable as you did ask and consult the warden before actions.
Atb Steve L.