A one year old is too old for a carrying car seat, or will soon be. Most of those max out at 30 inches or less; in the US, a boy will reach 30 inches on average on his first birthday, with a 95% range of 8 months to 16 months, and a girl not too different from that, according to the CDC Growth Charts. We're talking about a sitting-up carseat here.
The biggest problem is coats/snowsuits, as those are too bulky (and when worn under the buckles may be somewhat unsafe - carseats are intended to be securely strapped to the child, and strapping it as tight as it ought to be will be very uncomfortable.
One solution is to not wear the coat on the way to the car. Obviously, the child will be cold, so to solve that problem we dress them somewhat more warmly minus the coat.
In our case, the easiest solution is to take the cotton clingy pajamas and use them as long underwear. From sometime in October (a week ago here where I live) to sometime in April, most days our children wear two complete layers both top and bottom. They have fun Elmo or whatever pajamas on the bottom, on top of those their regular shirt and pants, and then on top of that a sweater. This keeps them quite warm - these are very tight pajamas, as they're cotton and not fire retardant, so they do a good job trapping warm air underneath. With this setup they often don't need a coat at all, unless they're playing in the snow, or the temperatures are very low; certainly the trip from the house to the car isn't long enough for them to get much of a chill.
There may still be a few days where you need to add a bit of warmth (if it's blizzarding outside!); for those days, either take the extra few minutes to don and doff the coat, or more easily, carry the child in a blanket to the car. That has the added bonus of a blanket that can be draped over them while the car warms up, particularly if it's not in a heated garage. Much faster than a coat to remove.