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Since this is a Camry, and most late-model Camrys are automatics, and I am not certain if they have rudimentary traction control or not - this isn't the most ideal FWD car for hill climbing.
OP, if you are going boondocking in the Colorado mountains, a Subaru or even better an Audi Quattro would be better on slippery slopes. The Audi, depending on exact model, could be high-maintenance though. How about a Subaru Outback? You could probably sell your Camry to someone from Denver. Or, keep it if you can stand having 2 cars.
Or, you could go 4WD instead of AWD - get some sort of 4WD pickup or SUV, one with "true" 4WD - including low range. If you don't use this truck for high mileage and don't drive it a lot except in snow, it need not be all that new or all that economical.
Some other FWD cars may have a form of positive traction or traction control, again I am assuming your Camry does not, correct me if I am mistaken.
deepcynic has a good point too, you have to modulate the power when traction is limited, the "feel" needed to do this is harder to develop with an automatic than a stick.
Chains have the disadvantage of being almost unusable on clear surfaces and limiting speed in any operation. They work well in snow and I have taken hills when my FWD is chained up that the guy next door cannot with his AWD and all-season tires, but I use them for emergency situations and don’t think they are suited for regular use. I ride with someone that has 4WD and real snow tires when it gets bad.