Mine will be outside (covered) for month of January in northeast. Wondering if cold winter weather will affect battery and if there is anything I can do about it
The battery itself will be fine until you get down to temperatures well below freezing (-20° C and lower). You won't damage the battery.
The problem is that batteries have trouble delivering and accepting high currents at low temperatures. So if the battery is cold-soaked, you won't be able to accelerate as quickly, and you won't be able to regen at normal full rate. You also won't be able to supercharge - the car will spend some time heating the battery first before it starts charging. But none of this indicates damage to the battery. It's just how they react in cold temperatures. If the battery temperature gets below -20° C, then I believe the car will start heating the battery (sorry, I do not have a reputable citation for that number, just random posts I found).
All that said, you should do as @PNWmisty
says and try to leave the car plugged in as much as possible. Teslas encounter some loss of battery charge when left sitting, whether cold or not. It's usually not too much, but there are sometimes bugs in the software that cause higher discharge rates, and it would be bad to allow the battery to run down too far. Leaving it plugged in allows the car to automatically charge the battery back up if the state of charge becomes too low. And if you do encounter very low temperatures, the car will automatically heat the battery up from "shore power" instead of using battery power. This will also allow you to pre-heat the interior of the car when it comes time to actually drive it, which is a great convenience.