BFG AT's will fill with mud almost immediately and do you no good. Even BFG MT's will suck not much later than the AT's. The only thing I've seen that works really well are Boggers or agricultural tires.

Is it mud or muddy holes filled with water? Avoid muddy water deeper than your hubs. You should repack your bearings if you spend a lot of time with them underwater. You can get crap in your alternator and kill it. Also you can get stuff into different emissions control sensors and get a check engine light. If you get the driver side fender deep enough you can suck crap into the intake and blow the motor.

Also you may throw of the tire balance with crud packed in the rim. Find a car wash if it happens to you and try to get your rims clean.

For recovery, make sure your doors are above water before opening. Take a spare pair of shoes and clothes. It can get real messy.