just to add to what others have said..
I've had 2 holidays in the north of Finland with my wife and 2 sons in 2008ish and then 2011. The first time we have 1 week in Ivalo (A national park on the Swedish border) and the second time, 1 week in Saariselka ( bit further up from Levi which we passed in the coach).
You need to think about what you are going to do when you get there. In mid-december I would imagine that it will be pretty dark and potentially very cold.
Both of our holidays were adventure holidays in Feburary half term where we did (between both holidays), husky sleigh driving (twice, no major poo problems), toboggans, , in-line sking, snow-shoe treking, 50km on a snowmobile (epic) some relatively gentle downhill skiing (ideal for beginners) reindeer sleigh ride though the forrest at night time (oh and 4 hours of snow and ice driver training in Sariselka in a souped up Imprezza, but that place is not there any more). All absolutely wonderful experiences but a) they cost a fair bit and b) you can't do most of them with a 1 year old son.
In Saariselka we had an absolutely beautiful log cabin on the edge of the town, complete with Sauna and everything you need. It was wonderful to get back to the warm cabin after a tiring day out (the cold can be draining), with some food and wine and to light a fire, have a warm, maybe a sauna and cook some food. Bliss.
We had an amazing and utterly memorable time on both occasions and it was great for the kids who have grown up in London, to see some proper snow and to have such an experience.
I would offer these thoughts to the OP:-
a) It was very expensive for a weeks holiday. There's the flight (we went to Helsinki and then had a 90min flight north), a coach journey to your destination, food is expensive, booze is very expensive (wine was at least double london prices in the state run Alko offy), eating out was pricey. All those wonderful activities cost a fair chunk of cash. I dont' remember the prices but I am sure we spent around 5-6K on each holiday.
b) Like Syla5 mentioned, your young son will obviously not remember his holiday at all. If I were in your shoes, I would save a holiday such as this for when he can remember it and enjoy it. Holidays with your kids are an investment in family memories. What's he going to do when he is there?
c) It was really cold at times. I mean on a warm day maybe -10 but on other days it dropped to -27C. At that temp, when you throw a cup of hot tea in the air, it turns to crystals and blows away in air and doesn't hit the ground. Imaging a nice sleigh ride through the forrest at night but feeling like your toes will drop off at any moment even though you're wearing 7 pairs of socks and fur lined boots. It's excillarating but when it gets down that low, you need to cover all exposed skin (and not wash in the morning and avoid water-based skin products). And that was in Feb, when it has lightened up a bit during the day (grey light). Without being a drama queen, personally, I'd not take a 1 year old there without extreme care.
d) If you are heading to the north (and not Helsinki), you need to factor in good quality thermal base layers to go under the winter suit, boots, fur hat and fur mittens that you will need to hire (more expense). We bought icebreaker morrino wool long sleeved tops and leggings. Cost a pretty penny but stil going strong.
. Initially I thought you must have stayed at a tourist trap on Suomenlinna or something, but obviously not. How did it cost over £1000?! Is that flights from the UK or somewhere further afield, because flights aren't so much - £100 or so, iirc.
and what's wrong with the island? A quiet and peaceful place a 15 min walk from the city centre. No idea at all about your assumptions of Suomenlinna 