Passes over the SoCal Mountains are usually kept open during snowstorms by plowing. Maybe an intense, once-in-a-decade storm would lead to a complete shutdown, and probably more frequently with the smaller, two-lane highways, but the road would be open soon after the storm ends. You'd be more likely to have roads closed by mudslides than snowdrifts. I would guess that Highway 62 would present no problems. Just be prepared for possible gawdawful winds in the Banning Pass. If you're lucky, you'll get tailwinds from a Santa Ana wind event, but headwinds are all too frequent. In that case, the freeway traffic is a big aid in creating a draft to help fight it.