For a week or two I had 33" tires on the back and 28" tires on the front of my F-150. That's about the equivalent of 4.10 gears in the front and 3.54 in the rear. During that time I got stuck on a muddy hill and needed to use 4WD. The truck was almost unsteerable. The different ratios meant that always both tires on one axle were sliding. Which axle was sliding would switch back and forth, and the net effect was that the truck pretty much went where it wanted regardless of where I pointed the tires. I was able to get up the hill and shift back into 2WD. But I proved, at least to myself, that mismatched ratios don't work on slippery surfaces either.
edit: The purpose of the mis-matched tires was to test how the truck would do with taller tires. I was going to lift it and put 33s on, but wanted to know if I needed to change the 3.54 gears. The 33s didn't fit on the front without a lift, but they did fit on the rear. So I changed the rear tires and drove it for a couple weeks, including a trip to tow a small farm tractor. I decided that the 3.54 gears were fine with the 33s and I didn't need to regear. So I put the 28s back on until I did lift it and could put 33s on both ends. I knew I couldn't use 4WD with the mis-matched sizes. But when I couldn't get up the hill, and knew that with it as slippery as it was it would never cause any bind problems I did it. It got me up the hill, didn't cause any problems (other than handling!) and gave me first-hand experience how bad that could be!