can share my experience with a Feb baby in Interior AK...the land of -50 or colder at times!
We did use one of those covers that went over the seat but not under the straps...but not consistently...I liked it better when I could see her more.
I dressed her in a long sleeved/legged onesie, a warm sleeper, padraig booties and a wool toque (pilot cap) with a fleece suit over top. Everything was fairly snug fitting so I don't think there was a concern with any ejection...but I could be wrong. Then I used two blankets, a wool and a quilt to cover her up once in the seat. I didn't ever carry the seat anywhere and left it buckled into the car at all times. I took her out and put her in a sling/wrap each time we left the car, under my parka. More often than not she was hot and needed less layers...but never cold. I always felt like a sheepskin under her in the seat would be great, but read in a few places that it wasn't considered safe.
All this said, if it was 40below or more...we tended to just stay home by the woodstove!
With this one, we are in Canada, so it's still cold, but not that cold. We will be using a convertable seat and won't again take it out...but I'm happy always to warm up the car and then put baby into the car with something similar to this set up above. Just need to find a good babywearing parka for our climate here...the one I had for Alaska is certainly too overkill for here!