you need chains when you go to mammoth, regardless of 2wd vs 4wd. The CHP has a checkpoint (whenever it's snowing) and they make sure you at least have them in the vehicle. If you have all-terrain tires then they dont make you put them on.
The difference between 2wd and 4wd is, the 4wd you dont need to put the chains on

Its tough (sometimes impossible) to drive a 2wd in snow without chains.
and drive very slow at first, get the hang of it!! A lot of people new to snow driving treat it the same as any other kind of driving, and rear end a car at the first stop sign they come to.... snow driving is VERY different than mud, sand, and dirt!!!