+1 on Michelin LTX and Tire Rack.

I have the LTX's close cousin -- Michelin Cross Terrain SUV tires -- and they are fantastic. Great ride, excellent in rain and snow (up to 14" of unplowed snow in my case). Have a little mud experience with them, but not much. My Element is AWD.

Tire rack is a great place for research. My Michelins were not cheap but they are terrific and slated to last for 70,000 miles, which I expect they will. I've had them on my Element for three years.

Good luck. There are lots of opinions on tires.