Is it safe to set my water heater tank to vacation during winter time? What else can I turn off to save heating bills during winter?
First of all you should turn off the water to the house and water heater . I've had a burst pipe at my vacation home because the power failed, it got really cold and froze pipes. When the power came back on and melted the frozen water in the pipes, there was a badly cracked pipe that did a ton of damage.   If you have pex plumbing that doesn't apply, but if it's copper or steel, you are at risk. Even if you did have a metal pipe freeze and burst, when you came back and turned on the water, it would probably be immediately obvious that you had a burst pipe that you could address immediately, mitigating further damage.
I would also set the heating system (not sure what you have, so take this with a grain of salt) to about 45 F. That's high enough to keep the humidity in check, but shouldn't be too costly.