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I agree with the suggestion about shipping your skis and boots, especially if you are not going to be using them after the Vail portion of your trip. Are you staying in LA for awhile or just making a connection there? If you are staying at a hotel in LA perhaps you could talk to them about having your equipment shipped there and stored as most hotels do have some sort of luggage storage facility. Hikers on the Appalachian Trail often ship supplies to US post offices that are in towns easily accessible to the trail so they don't have to carry everything with them. A lot will depend on your actual itinerary and whether you are stopping over in LA or just making a connection. You'll likely need to do some research and maybe think outside the box. I know it's always much nicer to ski on equipment you are used to but renting might end up being your best bet and the least hassle.
For longer term storage, there are many self storage units around the metro area. Not cheap, but then neither is paying extra baggage fees and lugging around extra stuff not needed for another leg of your trip, as it sounds like Terry might be doing. For example, I found "Downtown Denver Self Storage" with units starting at $45 a month. http://www.downtowndenverstorage.com/