Yes you can store it out side. Just remove the control box and store it inside and cover the unit, lift it off the ground so it is not sitting in snow or mud.
For smoking outside during the winter , if you can handle it the unit can too! (says the guy from south Louisiana) LOL.
since it is an electrical appliance ,i would not use it in the rain or falling snow w/o being under some sort of porch , tarp , overhang , etc.