Whenever my wife and I leave the house overnight - regardless of season - we shut the water off at the main supply valve. I relieve system pressure at one of the faucets before we go, but I don’t drain the pipes.
With the pipes full, there’s no worries about leaving the water heater on (though if we’re going to be gone for more than a day or two I’ll set the dial to “VACATION”).
I suppose with the pipes full there’s still a risk that freezing temperatures could rupture the system if the furnace craps out during cold weather. But:
-this is a pretty small risk
-if it happens, the amount of water that leaks out will be limited, since the supply is off
-it’s not worth the pain-in-the-ass to me of draining/refilling the entire house system to mitigate that small risk
-this is also why I don’t bother putting antifreeze in the drains/toilets during cold-weather absences
If your home’s water system has been shut off/depressurized for more than a day or two, some dissolved air may come out of solution and collect at high points in the piping. When you start running the faucets, these bubbles can create a water hammer effect: the air passing through the faucet lets the water behind it speed up, then when that water slams into the valve restriction, it suddenly decelerates, creating an intense pressure surge in the pipe system. This is similar to what happens when you shut a faucet very rapidly causing the water in the pipes to come to a very sudden stop; it stresses the piping, and in extreme cases (large air bubbles and high flow rates) can cause damage. When we return home, I try to run the faucets at low/modest flow until I’m confident that most of the big bubbles have been purged from the system. If you take the trouble to completely empty your water pipes before departure, then this will be even more of a concern when you return.
If you do empty your pipes, then yes, you’ll want to shut off your water heater completely.