I’ve been to Lapland several times, in Dec, Jan and Feb. The warmest it ever got was about -15C, and it dropped as low as -35C. We wore our normal skiwear (we are experienced frequent skiers) with the snowsuit over the top, and that just about kept us warm. On the very coldest days it is necessary to wear something that completely covers the face eg Airhole ski mask, to protect it against frostbite. This is mainly when the temperature drops when it gets dark, but remember that the amount of time the sun is above the horizon can be less than 4 hours in Lapland in January. So it is dark and cold a lot.
I cannot suggest a brand of jacket that will suit your son, you will just have to try a lot on. Decathlon are pretty good for soft fleece under layers and down liners at a decent price, but do not go for the cheapest stuff they have and don’t skimp on the quantity. I have a Decathlon brushed lining long sleeve top which is my absolute favourite of all the thermal tops I own (and I do a lot of skiing and other winter activities, so have plenty!) Also consider heated gloves - you can get them quite cheaply on Amazon these days. Buy thin liner gloves for underneath these.
If you are worried your son will not like to wear bulky layers, I would suggest that you practice at home (suggestion of the Snowdome is a good one.) In a place where the temperature can freeze the surface of your eyes in just a couple of minutes (PS get good goggles too! And try these on too, some have quite scratchy foam, some aren’t the right shape for your face,) you aren’t messing about here, you have to be prepared for the climate.
It sounds rather daunting, but it’s quite magical when you get there. There’s lots to do that isn’t skiing - husky sled rides, snowmobiling, snow shoe hiking. I’ve been on drives to see herds of reindeer and also wild moose. And it’s never going to be warm with scenery like this….. (taken at about 3pm - not midnight!)