An anti-siphon is a tube that is set up inside your tank. Under high pressure, as you probably know, CO2 takes on a liquid phase. Anti siphon lines are oriented for a specific bottomline so that when the tank is on the gun, and the gun is upright, the open end of the tube is out of the liquid part of the CO2 in the tank.
I doubt that freezing up the gun would do any permanent damage, although it could cause orings to swell, which could then be chipped by the parts that move around them. So damage, yes; permanent damage, no... orings are cheap, and they wear out anyway, after long enough.
When you shoot with CO2, the liquid CO2 must expand into a gas (for most guns). For a liquid to turn into a gas, it has to get heat from somewhere, in this case the walls of a tank. That's why you get frost on the outside. That's why if you shoot fast enough with CO2, you will generally get lower FPS after a while... there is less heat in the walls of your tank, so it is more difficult for the liquid to turn into a gas at a high enough rate to have readily availble CO2 gas in the valve. In some cases, the CO2 will condense into a liquid again or liquid will be drawn into the gun. This is very bad for consistent velocity. It also could cause the gun to seize from swollen orings (the CO2 will get into the urethane) and contracting metal.
Anyway- you probably won't have any major problems shooting CO2 except on cold days, or if you are likely to rip on the trigger for a while. I know back in the day I could shoot a slide frame cocker fast enough to get a fair bit of frost on the front of the body, so it doesn't take all that high a rof, just a sustained rope of paint. You'll get by, but switch when you can, I say.