What stats do you want? For stats to exist somebody has to monitor and count what actually happens, they don't just exist out of thin air.
There are stats about car seat misuse (based on random spot checks) which are shockingly high. That includes clothing rendering the straps too loose, but it's almost never given as a breakdown of ways car seats are being misused. However, loose straps is one of the most common ways car seats are misused. That can be because of clothing or because the straps are not adjusted to the correct shoulder position, escape artist child or simply people not realising that it is important to pull the harness snug to the child's body.
You can look at stats of number of children killed in cars, but that won't tell you whether they were in a car seat, what type of car seat or whether or not it was being misused at the time. Although we know that the numbers increase slightly in winter, which could also of course be related to there being more crashes in general in winter due to poor weather conditions on the road.
There are some more detailed studies which look at crashes where at least one person was injured and there was at least one child under a certain age in the car at the time of impact, and record the injury status and seat belt/car seat use of all occupants, and these are very valuable in terms of learning how car seats perform in the real world as opposed to in a crash testing lab. But it's very difficult to get detailed information about how the car seat was being used as the information is often taken from police and medical reports and it's not usually recorded whether the child was wearing a coat or how tight the straps were. People who attend crashes and immediately attend to children in seats are not usually the same people who are experts in how a car seat is intended to be used and may not be aware of such details to record them anyway.
You can find crash tests on youtube where seats are tested with dummies with the straps deliberately too loose, and you will see what happens in this case is too much movement of the dummy. In a forward facing seat that means much more stress is placed on the dummy's neck, which can cause injuries in itself, and the dummy will move too far forwards and strike obstacles in the car such as the seat in front which is almost certain death even in a 30mph crash. (It's equivalent to that seat crashing into their head at 30mph). In a rear facing seat the child will move up the seat itself and if their head is near the top they may also make contact with the seat in front. Or if the straps are loose enough to allow the shoulders to slip between, the child may be ejected from the seat.
Something I would recommend would be carefully reading the safety information and warnings included in your car seat manual. If you don't have it any more you can usually download it from the manufacturer's website. But this will usually have some warning about bulky winter clothing and/or placing any items (such as padded covers or blankets) between the child and the harness, which means that the manufacturer is aware of a risk from doing so, potentially from their own in-house testing.