Make sure thats not colder as there will be no heat circulation. If you open my Closets they're freezing right now. Its 17 here in NY & a closet is a room without heat. Another thing is that you asked if it will smell as you'll keep a Lid on the Tub. Well dont forget to Drill Holes in the Tub for air. Lil guy has to Breath hahahahaha
I live in pa and got frostbite trying to get dressed this morning. Just like you said,our closets are freezing