Puffy jackets are great in the Winter, but they cause a bunch of issues — when your child has one on, it creates unnecessary space between the car seat or booster seat buckle and your child, so when stopping short, or in a crash, that space then becomes room for your child to move more than they should.
To make sure this doesn't happen, use the "Pinch Rule": when you buckle your child in without a coat, you should not be able to pinch any material of their clothes between their shoulder and the buckle strap — if you can, there is too much slack in the strap. Tighten the strap so it's snug, and then try that buckle length when they have their coat on — if it seems too tight (or won't buckle) because of the jacket, remove it and buckle them in without a coat.
Pro tip: Hawker gears his own kids up for Winter with a thin fleece zip-up (that fits safely under their straps) underneath their coats, to make sitting in the car and transfers in and out of the car warm enough. Then after buckling his kids in, he puts their jackets on them backward, over the buckle.