For those that have been to other Western resorts (most of which require mountain driving), it's useful to know the lay of the land for Mammoth.
Almost the entire drive from LA (to Bishop, 40 miles before Mammoth) is in high flat desert, and other than in the rare circumstances of a major southerly storm this section does not have snow on it.
Once in Bishop, you go up from 5,000' to 7,000' on a very well maintained and not very steeply graded multilane highway. The Department of Transportation is very aggressive about keeping this road clear during storms. Chains are sometimes required on this section but in my experience that's quite rare.
Once you get to the turnoff to Mammoth, you are again on a very well maintained and not steep multilane road in a wide valley, and this gets you into Mammoth Village proper.
Much of the village is in the flat part of the middle of the valley, and you can in fact get to Eagle Lodge (one of the several places where you can buy lift tickets and start skiing) without ever driving up a steep hill (the road up to Eagle Lodge is very wide and straight and goes ever-so-slightly uphill). With my Subaru, I can generally get by in Mammoth other than in the most extreme conditions without ever putting my chains on--the condos that I usually stay at, the store, many restaurants, and Eagle Lodge are all in "the flats." Also, during storms, they are very aggressive about getting the roads clear as quickly as possible.
And in any case, Mammoth has a great shuttle system that you can rely on once you are in town if you don't want to drive, and it runs late, so you can use it to get to and from the slopes (at several of the base areas) and you can also use it to get to and from dinner/drinks/club if you don't feel like driving or if the roads are too snowed over to drive on.
I was just up there this past weekend and had a sunny Friday with 7' of snow from that week, then a stormy Saturday with 9"-14" falling (and I drove without chains and had no problems), and then a beautiful and sunny Sunday with the fresh powder to seek out all day.