Coats and Carseats

So my children have their first winter coats.
Which is an interesting thing to me.
My children have never had winter coats.
We had jackets, yes.
But never COATS.

So first off, thanks to Aunt April.

Second, How the F#$% do you get them in their CARSEATS with SAID COATS on?

I need to know! This is not a drill.
I mean,it's retarded to take their coats OFF and then put them back ON before they get out. And it's a pain in the ass. Do you just smooosh them in and make them fit?
Do you only put the coats on when you are really getting out of the car permanently but not bother with them for quick jaunts point A to point B?

Right now, we're opting to take them on and off as necessary but......this doesn't seem practical. How do all of you who are accustomed to the winter climate handle this?