Dear J B:
Please allow me to preface what I am about to say with my qualifications to say these things. I am a medically retired (read disabled) Physician Assistant & Midwife Certified in both PA & AK.
I have lived in Alaska and believe me it doesn't get any colder than that.
The bottom line with keeping your daughter warm is that if you have enough on, she will. In other words, dress your daughter in the same amount of clothing that you are wearing and she will be just fine, use the blanket just to get her to the car after that is when we would all like a nice toasty blanket, on the way to the car. I realize that gas prices are terrible right now, but let your car get warmed up before you have to go somewhere, if this means having an extra set of keys so you can leave a set in the car while it gets warm inside they are pretty inexpensive at Walmart. Personal experience tells me to use the new keys to start the car and leave it running, you know the keys you currently have open the doors. This might not always be the case with the new set. Only you know how long it takes to truly make your car warm inside to where you are comfortable. So, if it means you have to start the car 15 minutes before you would have to leave then that is when you start it, lock it go back inside and wait to go out. If I go into further times I would be blinding you with the obvious : )
I hope this helps you in one way or another, I think the most important thing to remember is if you are at a comfortable cozy temp, and your daughter is dressed in a similar manner, so is she.
Best of luck let me know how things work out.
J. T