Well since you asked…(this answer would probably fit better at a Dull Men’s Club).
There are a few facets to keeping an airport open in the winter. The big one obviously is keeping the runways clear, but that is a somewhat trivial task, and can be pretty easily predicted. So various air traffic flow control centers will keep the flow rate (planes arriving/departing) at a manageable level. If they see that an airline, eg. Finnair, wants to launch 80 planes between 1600-1700, but the airport can only handle 65, they will tell Finnair hold your horses, we can only accept 65. That causes delays, sometimes cancellations when the schedules simply wont work with things like pilot duty days and such. (Delay a flight when a pilot if already on the clock, and it’s possible the pilot can’t complete the duty day as scheduled).
This is the trivial bit. It causes delays and some cancellations (which do happen even in Helsinki), but usually they are not extensive.
The second part, and this is where Helsinki is world-class in their “snow-how”. When there is active precipitation or freezing obscuration, planes need to be de- and anti-iced. When this process is completed, the planes have what’s called a hold-over time, which means they have to begin their takeoff roll within a very specific timeframe, usually 10-60 minutes, depending on the type and intensity of the precip or obscuration. (this is literally timed by the second from the first application of the fluids). There are times when the snowfall is considered heavy, when there is no hold-over time available. During those times you have to start your takeoff roll within 5 minutes of the deicing procedure.
In Helsinki, the deicing facilities are a very short taxi distance away from the runway. So even at the heaviest snow events, the planes can still depart within the legal timeframe. You might have to wait in line for a bit to get to the deicing pad, but when they’ve completed the process, you are good to go.
Places like Heathrow which is known for their snow chaos events, and only 2 runways (which only 1 tends to stay open during snow events), the deicing happens like a 10-15 minute taxi away from the departure end of the runway, and there can be a huge backlog to depart because of the amount of arriving planes to the same runway. When those planes waiting for takeoff run out of their holdover times, now they have to taxi back to either get deiced again, or back to the gate, taking a gate spot from another arrival. You see the cascading effect of this.
There are other airports in the world where this is handled almost as well as Helsinki. Toronto and Calgary to name a few, I’ve flown a lot from those in the winter and they run smooth.
The problem if this process doesn’t flow smoothly is that if planes can’t take off, they take gate/parking space. So then you have to limit inbound flights, as there’s no point to land if you can’t park. Now ATC starts to hold planes, and when they run out of their normal planned arrival fuel, they have to divert to their alternate airports, causing all sorts of secondary issues.
Also, in Finland people generally know how to drive in the snow, so people working at the airports usually tend to get there. In places where snow events don’t happen that often, people generally don’t have a clue on how to drive on ice and snow, and usually they don’t have the equipment (winter tires and such) to do so either.
Now, when you have people who don’t show up to work on a snow day, even if your airport has the greatest contingency plans in place, if you don’t have the people to execute that plan, it all goes down to waste.
So, Helsinki is amazing in the wintertime because a) winter happens all the time so people know how to get to work, b) the airport design is such that it allows for a decent departure rate even at worst precip rates, and c) They have 3 runways, generally facing a favorable wind direction so they all can be used at a high % of days with the prevailing winds (when things get slippery, planes have various wind component limits as well).
I have lots of “fun” snow stories when flying planes. Did you know, that it can cost anywhere between €10-40k per plane to de/anti-ice an Airbus for departure. A heavy like what I fly can be close to 100k.
Ask me about that time when I had to de-ice 3 times and we still couldn’t go. That was 300k well spent.