Around here most of the oilfield trucks carry chains year round because the local oil roads turn to snot when it rains. In general, chains best suited for mud use are the HD ones with larger link size. It's not about traction, as any set of real chains (Not cable chains...) will do wonders in mud, it's about durability. Mud and associated offroad driving puts a lot more stress into the chains than snow driving. If you look, many of the chain manufacturers offer a "Mud and Snow" or "HD Mud Use" chain. It's got heavier links and will handle continued stress of getting you through.
I carry a set of medium duty chains most of the time, since we frequent the same roads, and two days of rain will render any normal 4wd immobile if it doesn't have a set of chains. When I lived closer to WY, I noticed that the hunters did the same in the fall, just in case they got into the back country and it snowed or even just rained a lot. You're not going to winch 20 miles back to civilization, but chain up and you can drive back through amazing amounts of snow and mud.
Here's why my truck is back on 265's, which will just clear chains... This was near Casper, WY, with a new set of 285 BFB AT's.
It was a dry road when we started down it, and then it started to rain. We went about 10 miles total, all in 4wd, slipping from side to side and trying not to end up in the ditch. I came down a long hill sideways, with the front of the truck in the middle of the road and the back in the grass and dirt, just praying that it didn't get dragged off farther. Though I was impressed that the BFG's got me though, chains would have helped immensely. You don't get this kind of snot after a rain in the midwest, where "dirt" roads are actually gravel, but out here in the wild wild west, dirt roads are dirt and clay, and they're a mess if they're wet for long...
Winching will get you through a "mud hole", but I don't think that's what the OP is talking about... I invite you try winching down 20 miles of snot slick desert road with nothing in sight but low scrub. Good luck!!
Chris