Well there's a number of different things that "could" happen--personally I would let it run (circulate) and when the water goes inside, the water will be heated by the air--plus circulating water won't freeze.
If you drain the water, the exposed metal inside will begin to corrode as soon as the water is emptied...Plus how could you ever make sure ALL the water is out of all your underground lines???...I guess you could call the lawn sprinkler company and they could evac them with air--but again not practical.
The expense of antifreeze in the amount of lets say 100-150 gallons of antifreeze @ $10 a gallon...well that's out as far as I am concern.
The only problem with letting it run is if you develop a leak--then the water would not circulate and begin to freeze and cause all kinds of problems....Or if you have a lengthy power outage, the system will once again begin to freeze----
IMO anyone not having the ability to pay 100% attention to the system--will encounter a lot of potential problems.