I've been "airing" my system for years...no problems, but, you must be thorough in the process, but, then again, you have to be thorough with the pink stuff, too.
Your fresh water tank has a drain valve in it...you'll need to crawl under the TT to see it, but, first you should open that and let your FW tank drain out onto the ground. There may be a little water left in it, but, the volume in that big tank, if frozen, won't do any damage. When the FW tank is drained, run the water pump for a bit with a faucet open...it will clear the pump lines of water and it won't be damaged if run dry for a bit.
Next, go to the water heater (relieve the pressure in the tank first by opening a hot water faucet or pulling the relief valve). Throw your water heater bypass valves to take the tank out of the system. Remove the anode rod and plug assembly and let the tank's water drain onto the ground. While it is draining, open both the cold and hot water low point drain valves up. Go inside and open all of the faucets and hold the toilet flush valve down...this allows most of the water in the system to drain out onto the ground through the low point drains (that's what they are there for). By now, the hot water tank is drained...you either leave the little bit of water in there, or, I flush clean the tank with my garden hose and special curved "flush wand" for water heaters (you can get one at any RV shop). You'd be amazed at the amount of "crud" that accumulates in the tank. When I'm done with that, I've got that trusty syringe (I've actually got a bunch of them for use in my shop) and vacuum line hose and I suck the remaining water out of the bottom of the water heater. While I'm cleaning the water heater, the water has been draining out of the low point drains. When done with the water heater, I install the drain plug / anode assembly and it is good to go. I then close the low point drains, close all the faucets and hook up my air compressor using the adapter (again available at most RV supply houses; get the "no hands" type, your air hose from your compressor can hook up to it with a quick connect). Set air compressor for 45-50 psi and turn on. Go inside and starting with the faucet closest to the the shore water hook up, open it up and let "run" for a minute or so. Hot and cold. Close those, go to next faucet and repeat. Do the toilet and then go outside and do the "optional" outside shower port. For added "safety" I do a quick once around again on the inside faucets. Then I open the low points and let them run for a couple of minutes. While the low points are blowing the last vestiges of water out, I go inside and put 1 cup of the pink stuff down each drain (for the P traps) and a cup in the toilet. Turn off the air compressor and put it away. Close the low point drains and I'm done.
Sounds, complicated, but, once you've got the routine, it can be done almost as quickly as using the pink stuff; you've got to cover the same ground to put the stuff in as I do blowing the water out. A gallon of the pink stuff lasts me about 3 or 4 years, no pink stuff left in any lines next spring.
That's the way I do it. There are many that fear that there may still be enough water left in the system to cause damage...I've not had that problem. There are many that believe and trust in the pink stuff...that's fine, too, as I never had a problem with it back when I did the "traditional" winterizing, but, I could taste it, no matter how many times I flushed the system for the first couple of trips. The only time I couldn't taste it was when I "overdosed" the system with chlorine trying to get the taste to go away. I must say, I don't like the taste of chlorine any more than I liked the taste of the pink stuff...