welcome to genvibedifferentials in cars allow one wheel to move at a different speed than the other. If you had a fixed axle locking both sides, you would eat tires unless you drove perfectly straight all the time. I have had the one wheel spin, one wheel stationary in low traction in a lot of vehicles, the worst was my RWD pickup truck that could get stuck on wet grass if there was nothing in the bed. How Stuff Works is a great site, check out
http://auto.howstuffworks.com/differential.htm for their description of differentials. a limited slip differential would probably help, but I don't know what the cost would be, or if it would be worth it. It wouldn't be for me, because I don't race, and if the roads are icy enough to make the car get stuck, I tend to stay home.The pull to ths side under hard acceleration is probably what is called torque steer. I don't know why it happens, but mine does it a little. I notice it most when really acelerating hard, then shift, and as I let the clutch out the car feels like it wants to swim a little bit. There was another thread here on that but no real solutions other than expect it and deal with it.
http://forums.genvibe.com/zerothread?id=9726Sounds like the roads were pretty bad on that mountain.