I am riding on Bridgestone Dueler H/T's and my runner is equipped with 4wd. I've never driven in snow/ice conditions before, but i'm planning a trip to Big Bear Mountain in January and i'll be driving. Do I need snow chains??
You should be fine without them depending on the conditions. If the conditions get bad enough they will require all cars to have chains regardless of 4wd. You just need to take it easy, don't brake hard and no sudden turns or movements. The roads should be cleared up there so you shouldn't run into any problems.
You also could get some chains, keep them in the back and return them when you get home if you didn't use them. Just to be safe.
It depends on the weather really, but it's always a good idea to carry chains when you're in the mtns during winter. If there's snow on the road and you don't have any, you'll get turned around at the chain check anyways. Usually you won't have to put them on, but they'll check to see if you have them.