I looked into this a while back for one of the parents in my cub scout den. At least here in FL you can easily get away without the humidification except maybe in the middle of winter. This is normally the only component that must have 120v wall current. The main body of about every CPAP is just a small DC air pump. Most every one will either run on 12 volts or sell a reasonably priced cigarette lighter adapter style power supply.
A unit that will run on straight 12 volts is pretty easy to deal with. Ebay and other sources sell a huge variety of sealed lead acid, NiMH, or even lithium battery packs. With a little ingenuity you can easily adapt your unit to run on one of these. The only concern will be the battery capacity you'll need for your intended trip. One that requires a power supply (much like a laptop) will weigh a bit more and probably be somewhat less efficient.
I pretty much figured out that with my friend's unit he could easily run it for a night off my car jump-starter (an 18Ah sealed lead acid battery). Something like this would be fine for car camping but I don't think a really suitable solution exists for backpacking.