CO2 is out, as it needs warm temps to work. At -10, it might not get the pellet out of the barrel. HPA might work, but you would need to have an efficient air dryer to remove the moisture from the compressed air. Otherwise you risk iced up internals. A good PCP set up with gun and accessories for filling will cost at least twice the $300 limit. As for springers, cold temperatures aren't neccessarily good for them either. The lubrication in the spring mechanism will thicken, and may cause a failure. A decent pumper seems to be the answer. If you are hunting rabbits, birds and other small game, something along the lines of a Steroid-modified Sheridan is what you want. It will send a 14.3 gr .20 pellet at near 800 fps regardless of the weather. It will easily take on critters up to raccoon size. Even a standard Sheridan will be fine, they are easily found on the airgun auction sites for around $150 or so.
