They will indeed work in mud. I've used them on 1 ton trucks in snow, ice, and mud. They won't work miracles, but they will generally get you that little bit of extra bite that may get you where you need to be.
The are a few problems though:
#1. Ride. Unless the surface you're on is super-soft, the ride is very rough.
#2. It's hard on the tires. You can rub holes in the sidewalls of your tires if you leave the chains on long enough and don't pay attention.
#3. It's hard on the chains. Their lifespan is generally measured in hundreds of miles, not thousands. As tire sizes get bigger, chains can get a little pricey.
#4. It's hard on your differential and axle shafts. When chains bite into the ground, they BITE. This puts added stress on the differential when you turn.
#5. It can do VERY bad things to your fenders. If part of a chain breaks loose, it can cause HUGE damage to your bodywork in a very short period of time.
#6. It's hard on the trail. Running chains on anything other than frozen ground will tear the trail up in a big way. If the amount of mud on the trail indicates that I'll only make it through with chains on, then I'll turn around and go home instead of tearing up the area.
#7. Pain in the butt factor. Putting chains on is about as much fun as changing a tire when your spare is mounted under the vehicle. Do you really want to do that in the mud? Also bear in mind that you'll be stopping to check tension on your chains 1 mile after you first put them on, and then again hourly after that. At least if you want to avoid bad thing #5 that I mentioned above...
#8. Speed - you don't want be traveling any faster than about 20 MPH. Going faster than this with chains on will dramatically increase the chances of the above issues causing big problems for you.
#9. Foresight. Chains are best used before you get stuck. Sometimes it's hard to know when that "stuck" is going to happen. You may need to spend a LOT of time shovelling if you are trying to put chains on after you get stuck.
Some heavy (as in Peterbilt size) trucks run chains for longer periods of time on logging roads or oilfield roads - but that's a different animal in terms of how heavy the chains are and the type of vehicle that's running them. Every trucker I know agrees that chains are the only way to go certain places...but they'd rather not use them if they don't have to.
I personally carry two sets of V-bar chains (front and rear) in my Jeep during the winter months. They're "required equipment" for many of the winter trail runs that the Jeep club I belong to does, and they're the best way I know of to stay mobile when the weather in the mountains truly goes downhill. They're required in some areas of British Columbia if you're not using specific "winter tread" tires...not that I think anyone is going to ask me to see my chains when I'm driving an obviously modified Jeep. :smiley_drive: