Summer Tires and chains
 

I am going to the mountains in Mammoth Ca in a couple of weeks. My new NX300 F Sport has Bridgestone Dueler H/L 33 235/55r 18 100V tires on them. The Lexus sticker calls them summer tires. When I look up at Bridgestone site they are say all season except for extreme cold. I will also buy some chains/cables for them. Is this ok for these tires. Whats with the summer tires reference in the Lexus sticker. Also what brand chains/cables would you recommend and is it ok to use these tires for the snow with chains? How good do they hold without chains?

Is it AWD or FWD?

Use cables, not chains, if you have to. Pain.
Personally, I go to a junk yard tire places and find cheap rims and winter tires. Have them mounted onto cheap rims and put them on winter time. It's very easy to do and you can drive that way for long time. I just bought set of Dodge RAM rims for $26 each. $15 was mounting and balancing. So now I have 2 sets of tires fo rthe truck.
But anyhow. You will not get far on all season or summer tires, on real snow or iced road. Of evils you mention, go with cables, they are much less devastating on tires and suspension, than chains. As you will be using them like once or twice in your life, go buy some at Walmart. Maybe even return them after use. Walmart has very slack return policy.

I just purchased a set of cables today for my Nx200t at Napa Autoparts store. Depending on conditions, even a 4wd/all wheel drive vehicle with all terrain or snow tires may be required to have cables/chains.