Mom's front hay pasture has eaten a variety of things. I know we got a tractor stuck in it a couple of times, although I think it was the old International 2WD tractor.
I'm sure we got a hay swather stuck. And, a year or two ago one pickup getting hay got stuck.
One old option is to tie wood fence posts to the rear tractor tires like super tire chains. However, you MUST back out. If you drive forward, you risk the torque lifting the front end of the tractor which is extremely dangerous. Backing up the torque pushes the front end down.
I think the older tractors could walk themselves out of a lot of woes with the bucket. However, I'm not sure the bucket on my Ford is strong enough to do much crawling.