We, or I don't shoot my guns in a vacuum. And although it may not be enough difference to feel, wouldn't a gun recoil harder in cold dense air than in warmer air?
The pressure in the barrel, even with 100% combustion, will still be in the thousands of PSI when the bullet exits. Atmospheric pressure, despite variations in temperature, will be very close to 15 PSI,one atmosphere, 30" of mercury, 760 millibars, however you want to represent it). The only significance air has is the 15 PSI pushing on the pointy end of the bullet in the barrel vs the combustion gases in thousands of PSI pushing on the other end.
That 15 PSI is pretty constant regardless of air temperature. It does vary slightly, less than 10%, between hurricane weather and a bright sunny day. Theoretically at least, recoil should be slightly higher in a hurricane when the barometer says 13.5 PSI. The same is true of high altitudes vs sea level. That 1.5 PSI atmospheric difference gets lost quickly when compared to the pressure on the base of the bullet which is in the thousands of PSI. I seriously doubt that it would be possible to measure the difference in recoil between a rifle fired at sea level on a sunny day and the same rifle fired atop Mt. Everest in a hurricane.
If air was not a factor in recoil, a brake would do nothing to reduce the recoil
Sorry but that's incorrect. A brake gives escaping gases an exit other than through the end of the muzzle. The more gas that gets bled off perpendicular to the barrel axis the less there is to generate thrust,secondary recoil). If you want a really effective brake, angle the ports more toward the butt of the rifle similar to those on some 50 BMG's. The force then is partly directed back from the muzzle which partially counteracts the thrust from gases exiting the muzzle. But please don't use the bench next to me.
Air has nothing to do with how a muzzle brake works. A muzzle brake would work just fine in a vacuum,I know, you don't shoot your gun in a vacuum but many physics examples use a vacuum as a standard reference - then things like air temperature don't confuse people). Plus, you wouldn't be able to hear the ungodly noise since sound waves require a medium to travel through.