The first pic of the chain going with the tread is not as good on ice as the "ladder" style that all chain goes across the tread. The chain going with the tread, on ICE, will slide more with the direction of travel. It's not supposed too, but in my experience with ice conditions on front, it does. Generally, in those areas of travel, wet snow is more prevalent then true ice covered roads. With 4x4 you really should be fine and some of those mountain pass's allow 4x4 with no chains. The best option is to not drive when conditions are slippery or icy. It likely would only delay your trip a day or less (unless there's some freak snow-ma-gedden. On Ice, chains or not, it's just bad to drive on. In those areas and wet snowy conditions, everyone is going slow 20mph or less and 4x4 will work just fine. On true ice, all bets are off (chains or not) . . . .

ETA: That east / west route may or may not be open to drive in the winter - Also, it's not uncommon to close roads in snow/ice events and delay all travel till road clears