I wouldn't travel through any mountain roads on fresh snow without chains, honestly - twisty hairpins, steep grades, etc. Snow tires are great, and xDrive is wonderful... but it all has one limitation - a small patch of rubber that needs to touch the road.
The laws in the US for tire chain use varies from state to state, which can get confusing. Some states have absolutely no laws, others have "permission" provisions, while others may have requirements... some others yet have provisions limiting the use from dates, while others may limit based upon snow condition. It gets a bit complex. Here in CT, where we see a fair amount of snow, I've rarely seen vehicles with chains. Most people will opt for A/S or snow tires, and that seems to work. That said, most every road is plowed, and even with snow storms that put down 6 - 12 inches, most cars aren't traveling over roads that have more than an inch or two.