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If you are planning to travel down I-5 to LA because its an interesting route with things you want to see, that's fine. However, if you are taking that route because you think it would be less likely to see bad weather, then you aren't really going to help yourself.

I-5 crosses several mountain passes between Washington and Los Angels, and the highway can see significant storms. The mountains at the Oregon/California border are most noted for bad weather, although I-5 can even occationally close going over the Grapevine between Bakersfield and LA. I-10 also isn't a worry free route. Snow, and even more likely, Ice is certainly a possibility as you make your way through Arizona, New Mexico, and West Texas.

Certainly, it is worthwhile to check the weather forecast in the days before you leave, and try to route around a major storm. However, since winter weather is possible almost everywhere in the US, generally your best bet for winter travel is simply to take the most direct route. That puts you on the road for the shortest amount of time, which is really the best way to reduce your likelyhood of hitting a storm.