Winter gear for baby when running errands

FTM here so I’m looking for what works for other moms. My 4 month is is almost 17 pounds, so her infant car seat carrier is starting to get extremely heavy. What do you all do in winter when taking your baby to run errands or into restaurants as far as coats, blankets, etc. If I leave the car seat in the car and just take my baby, the “put blankets over your baby in the car seat carrier to stay warm” wouldn’t work since I’d be leaving the car seat carrier in the car. I know you shouldn’t put the baby in a coat while in the car seat, so do you get inside the back seat and put the coat on before taking the baby outside to go into a store or restaurant? Do you wear the baby in a baby carrier on your chest? Coat on? Coat off? Wrap them in blankets? Thank you!