Cold doesn't damage the battery. Batteries are basically electricity pumps. When they're cold they're less willing to give up their electrons. But being cold isn't inherently good or bad. It essentially reduces the efficiency of the pump.

Generally speaking the thing you want to avoid with ev batteries is getting them too hot. Heat damages them more than anything else.

The next temperature related thing is putting a heavy load on the battery when it's too cold. The important thing with this is a cold battery itself isn't necessarily bad, it's putting a heavy load on a cold battery that's bad

Also generally speaking, the healthiest state to store a battery is half charged.

If you'd like to read up on it the thing to search for is "lithium plating."

So long story short, if you're going to leave your EV for weeks at a time, the best thing you could do is leave it plugged in to a wall outlet and set the charge limit to 50%. Remember, EV batteries don't lose electricity when they're cold, they just can't pump all the electrons in them because they're cold. If you leave it plugged in and set the charger limit to 50% it'll maintain the battery at a good state of charge. It won't draw that much electricity either.