My daughter was born at the end of October and I didn’t really need anything special. I was given a ton of newborn hats but didn’t use any of them. Just the basics, like long sleeve onesies and pants. Just depends how cold it gets I guess

Snow suit or jacket BUT as for the car seat safety aspect I believe you'd need to remove her from it if it's bulky. To test the safeness have her in it, strap her up properly (tightened) then unbuckle her remove the jacket/suit and buckle her again. If it's loose it's not safe.