I'm in North Dakota, so I understand COLD!!
What I've done for years with my kiddos is this. I buy them thin fleece or thermal type jackets to wear in their car seats and a heavy winter coat to bring along. Once they are buckled into their seats I help them put their coats on backwards until we get to our destination. Once we arrive I have them put their heavy coats on over their thin fleece/thermal jacket for the trekk outdoors. It's annoying at first, but we all adapt in time. It is harder when they are all young and need help zipping up, but it gets easier as they got older.
Supposedly you can get kids into their seats safely with coats if you put them in with it unzipped and then slide the straps over their shoulders, buckle, and then zip up the coat, but I found this to be impossible. I read about it on carseat dot org You may want to go over their and ask them about it, but I couldn't get it to work for me.
I imagine your infant is still in an infant seat that you carry with you, right? Or do you have her in a convertible seat. If she's in an infant seat you might like something called "Bundle Me."