I don't know if this affects you, but the lightest batteries with a given capacity seem to be "Lithium Ion" batteries - which work poorly in very cold or very hot weather. Not only do they have reduced capacity, but the batteries may be damaged. I've had this problem with cell phone batteries left in a car.
I think keeping a SEALED lithium ion battery in your sleeping bag, as another suggested, maybe with a plastic bag around it, sounds like a fairly good solution - though if it gets cold enough, the battery will be damaged when you aren't in the bag - unless you keep the battery inside your coat the rest of the time. Obviously, do not put the CPAP machine in the bag - it wouldn't be able to pull in enough oxygen.
Would it be too heavy and bulky to carry more than one battery? BTW, if you use a power station that creates 115VAC, the battery may be replaceable - so you could carry two with just one power station. Likewise with UPS (uninterruptible power supply) units, but most UPS's use lead acid batteries.
A big 24V deep cycle marine battery would likely work - or two 12V batteries in series. But it would sure be heavy, if you are backpacking, maybe even if you are sea kayaking. And if the acid leaks, that could be a big problem. (Both because of the damage it could do, and if you are sea kayaking, salt water mixed with acid releases lethal chlorine gas.) But it might be OK if you are car camping. I confess that all my recent winter camping has been in a vehicle.
I am going to assume you wouldn't be asking this question if you were going to be in a campground with an electrical connection.
BTW, my AirSense 10 uses a lot less electricity if I don't use a heated hose, based on power and energy draws measured by a "Kill a Watt" power monitor. They also use less power if you reduce the pressure, though it will be less effective. I haven't tested how not putting water in the humidifier affects power draw. Also if I sleep less long, so I don't use the machine as long - even if I stay lying down while awake.
Online info says the AirSense 10 machine uses more power than some of the others.
Perhaps you could use a solar charger during the day - but they take weight and bulk too. And are ineffective if covered by snow.
I've been playing with non-CPAP solutions. You may want to experiment and see whether any or a combination of them work well enough.
I assume your sleep apnea isn't so bad that experimenting could kill you. E.g., high wedge pillows (some are inflatable, so are light and pack compactly; also try sleeping while sitting), pillows made out of foam custom cut by you to your face, so you can't sleep too far to your side or on your stomach (which tend to cause your chin to dip - one of the main causes for some people of sleep apnea), neck braces, so your chin can't dip, a mouth guard combined with a mask that fully covers your mouth and nose (I use a ResMed F20; If you don't use the CPAP machine, but do use a mask, use a much shortened hose, so you still get oxygen exchange, but having some hose helps prevent you from sleeping too much on your side or stomach), which work together to keep your mouth closed. In my case I breath better with my mouth closed. Also - any mask that doesn't completely cover your nose and possibly mouth wastes energy, because some of the air leaks.
A non-CPAP solution would save you the bulk and weight of both the machine and your batteries. But you would need to experiment too see if any work.
I'm sure other people have other ways of helping sleep apnea, that might allow non-CPAP solutions.