For ice or mud? If ice traction is what you are looking for, try a good
ice/snow tire with studs. Studs may be illegal where you live, so check.
Need more extreme you could switch to a spiked tire, 1-1/2 long spikes are
common.

For mud, there are lots of really good mud terrain tires on the market. Look
at the BFG MT. If you need something a little more extreme, super-swampers
are nice. I would also recommend getting beadlock rims so you can air down
lower if required. There is one set out there, IIRC, that are DOT approved.

I would get no less than a 31x10.5x15 tire, so you're likely going to need
to install a lift. 3" should do.

Steve

check out tire rack

Do they still make the cable chains?

They were made from 1/8 inch or so steel cables.
I haven't lived in cold country for awhile so I don't
know if they are still available.

There is a VERY good reason they warn about tire chains on the Bravada.
Being it has open differentials on both ends and the open unit in the
transfer case that gives you the AWD it is easy to lose control of the
vehicle when the traction shifts around between the tires because of the
chains. Oh and by chains they mean ANY type of tire wrapping traction
aid. That includes cables or stud belts.

What you will probably need to do is get a set of steel rims, and mount
up 4 GOOD studded snows for it. That way you don't end up destroying the
drive train.