The day DD was born it was -40 outside.
Depending on what temperature you keep your house at, and how cold it gets where you live, you may not need to do much differently. So many places you go have the heat up so high you just need to keep babe warm getting from the car to inside. The best thing for that is just a really, really good blanket. You shouldn't use snowsuits or coats with a car seat (they get compact on impact and make it so the straps are no longer the right tightness). And trying to bundle up a baby and then unbundle them and lug around one of those itty bitty snow suits or buntings is honestly just a pain in the ass.
So yeah, wrap baby in a very warm blanket, make sure you've got a hat, and hurry in and out as best as you can and you should be fine.
I will say this though, originally we weren't going to buy a bucket car seat. We bought a convertible one. Then DD was born and we soon ended up buying a bucket too because it was so much easier to buckle her in, then bundle with a blanket, THEN take her out to the car than it was to bundle her up, take her to the cold car seat in the car, unbundle her to buckle her in, then bundle her up again.
You might want to try DIYing one of these (looks super easy): http://www.imperfecthomemaking.com/2012/01/tutorial-hooded-car-seat-blankies.html <---Use some polar fleece and it'd be PLENTY warm, plus polar fleece doesn't fray, so you wouldn't need to do as much sewing. You could leave edges unfinished. ETA: If you're using good, warm fleece, you can skip the double layer with batting...even less sewing! In fact, at that point you almost have a new-sew project, just need to stitch a line to make the hood. And if you were still worried that it would be too cold out, you could use this in combination with one of those car-seat cover thingies (like this).
As for clothing, unless you don't want to bring babe out in PJs (which many people don't), footed sleepers are great for everyday! Babes have a way of losing socks, but those sleepers make sure little feet are always covered. And if it's extra chilly, you can put a onesie on underneath as an extra layer. Once the weather warms up, you can cut the feet off and hem the legs, which also allows babe to wear smaller sizes for a bit longer.