I'm not sure if the distance from LA is doable, but South Lake Tahoe would probably be the place to guarantee snow - it has a ski resort there which had just closed for the Summer in June last year. Its about a 2 hour drive from San Francisco, but I'm not sure how far that is from LA
LA has three or four of fair to large sized ski resorts nearby - Mountain High, Snow Valley, Snow summit, Big Bear etc. Normally fairly snowsure but if you decide to go, check out the conditions first - Tahoe is a fair distance but I agree with hmboughton that it'd be a fair bet that you'd see some white stuff!