I've struggled with this myself. I think it's especially difficult when they most out of the infant carrier because even a light coat seems so bulky compared to their small size. But now that my kids are a bit older, I feel completely comfortable with them wearing a fleece jacket under the straps with care (as in I try to smooth/pull out excess fabric and pull that harness tight) and with our heaviest 300 weight fleece, I do prefer to do the car seat trick, so that less of the fabric is under the straps. In addition to the fleece jackets, we use hats and mittens and keep a fleece blanket in the car for each kid. Jackets are from Land's End, kid sized blankets from travel section of Target, but you may want a warmer blanket. Most of the time the fleece with accessories are fine and I try to dress the same as them to make sure that's the case. However, for those snowy school days, they require she have a real snow jacket for recess, so I park and, as quickly as possible, help my daughter into her snow jacket with the door open. I do worry about her getting too cold, but I worry more about her being in a bulky jacket. Probably soon she'll be able to do this on her own (unbuckle and put it on), so she could do that while the car is still running and door is closed. And another option would be to wear the fleece and send her snow jacket, but I think it would be too difficult for her to keep track of 2 jackets.
I hope this helps! I'm always interested to see what others are doing and open to improving our method, so I'll be keeping an eye on this thread.