Subject line says it all. Or, I guess it would be better put as: “What weather conditions would close an airport; what would cause massive delays, and what’s no big deal?”
For example, if there’s an inch or two of accumulation of snow on the ground, is that enough these days to cancel flights and tie up schedules? What about snow and high winds?
To the snow part of the question, the only answer is “it depends.” Some airports are very well prepared to deal with frequent snowfall (I’m thinking Minneapolis/St. Paul, for example) and others come to a screeching halt if a flake flutters down (Atlanta, Georgia?).
The impact to schedules is also related to the runway layout. For example, here in the DC area we have 2 airports: National and Dulles. The runways at National cross each other. If one is closed for snow removal, the other must be closed too. Everytime the runways are cleared, 1/2 hour is lost off the schedule of every airline at that airport. In contrast, Dulles has more runways which are parallel to each other. Snow removal can proceed on one runway while the other is used for takeoffs/landings. So, there might be some delays but the planes keep taking off and landing steadily.
What closes airports here in NZ is fog. A few days ago, we had fog hit Wellington’s airport, the capital, for several days in a row. Shut everything down. (Unusual as it’s summer.) Fog usually blankets Auckland Airport for a few days each winter.
Say what you will and joke about Buffalo weather but it takes a major amount of snow to close the airport. I read in the paper a few years ago about a conference they hosted and people came from Russia to learn how to keep the airport open.
Not answering the OP but I had to say it. The few times I hear on the radio that the airport is closed is almost always due to ice.
In Buffalo, it’s very, very heavy snow. International conferences regarding inclement weather and airports are often held in Buffalo, and BNIA is held up as a model airport when it comes to snow removal – they approach snow with a brute force attack, meaning tens of massive snowblowers, a lot of chemicals, and timing takeoffs and landings so the blowers can continue clearing while the airport remains open.
Every couple of years, the snow falls faster than it can be removed. The airport is forced to close. BNIA’s runways are short, and they cross each other, so as with National, if a runway is closed for snow clearing the other closes by default.
Wow a concurrent post positive about Buffalo. Who da thunk it?
I was in Des Moines on New Year’s Day and we had to wait an hour for the ice to be removed from the runway. If that had happened in Memphis, it would have taken longer. 
The right answer will usually be “It depends.” Aircraft need acceptable visibility, a surface safe for landing, braking and taxiing, and clean (i.e. deiced) wings and tail surfaces prior to takeoff.
Some airports have landing systems that allow some aircraft to operate in close to zero visibility, so these may not completely close in conditions that would have others shut down. But you could be sure that the rate of operations would be slowed and produce considerable delays.
As noted, you can expect that equipment for dealing with snow & ice will vary a lot.
On an approach to none other than Buffalo one stormy night, we circled for-EVER and were about to divert to another airport because the wind was over 55 mph, as I recall. (55 knots?) Anyway, the windspeed apparently dropped to a 54.99 mph crosswind as we landed at Buffalo with the nose of the plane pointed not exactly 45 deg off the centerline of the runway, but it felt like it. I recall hoping it was not too cold out there, since I knew for a fact it was raining, and I knew for a fact the plane was going to crash, and I didn’t want to be wet cold AND bleeding.
That’s okay, the fire would have kept you warm.
If only I had thought of that I would have been so concerned!
If only I had thought of that I wouldn’t have been so concerned!
And somewhat favourable wind conditions. I remember being delayed once at San Francisco airport due to nothing more than rain and high winds.
Good point, though perhaps this should be phrased as “not too unfavorable”.
Winds that are steady and more or less down the runway can be strong without creating unacceptable problems. Severe crosswinds, gusts or wind shear can and have created havoc, and could easily be the reason for closing an airport.
Another “it depends”.
Snow that would close a Florida airport is barely noticed at, say O’Hare or St. Paul, MN, or, yes, Buffalo, NY. On a related note, slickness of the runway - due to snow, ice, rain, or anything else - can also cause major problems and different runways have different characteristics. For instance, some are grooved to provide better traction in slick conditions.
Winds are another factor - much above 45 mph as a crosswind is getting serious for anyone, and at a certain point operations have to cease.
Equipment - both on the airplane and on the ground - is also a consideration. There are some extremely sophisticated systems that, as mentioned, allow operations in almost zero visibility. However, if the airport is lacking those systems then the visibility limits are dictated by what equipment they do have.
Everyone thinks of cold and snow - but excessively HIGH temperatures can also effectively close an airport, most notably at high altitudes. Hot air is less dense than cold, and high altitude air less dense than low, and a combination resulting in very thin air can ground aircraft for the simple reason they become unable to generate the necessary lift to leave the ground.
Who flies there - different airplanes have different capabilities in regards to weather.
As a comparison - O’Hare airport in Chicago rarely closes (but when it does - boy, howdy, do people notice!). It has heavy equipment for snow removal, up to date de-icing equipment, various forms of radar and weather monitoring, a multiplicity of runways, and the most sophisticated instrument landing systems available today. My local airport, the one I fly out of, has much shorter runways (actually, it only has one), the “snow removal” consists of a plow on the front of a pickup, no de-icing equipment (other than a heated hangar and human elbow grease), we use the weather monitoring at another (nearby) airport except for windspeed and direction (we have that on the field), and our “instrument landing system” is the runway lights. We close a lot more often. But then, it wouldn’t make sense to upgrade - virtually all of the airplanes flying out of there are small and lacking in either anti-icing equipment or sophisticated instrument landing systems.
So… the most succinct answer (after all that) is that the decision is made based on safety issues - what’s a safe limit for the airplanes flying in and out, based on weather, airport equipment, airplane equipment, and other factors.
It is also worth noting that individual flights can be delayed due to weather in between airports rather than at one of them. For example, I was once on a flight from Newark to Indianapolis which landed abruptly in Dayton, Ohio due to thunderstorms. Passengers were irked but understanding as long as it was raining in Dayton. When it stopped raining, and people on cell phones had confirmed that it was not raining in Indy, some passengers got very upset. They didn’t want to believe that dangerous conditions could exist somewhere in between the airports.
Detroit Metro airport isn’t the snow-clearing ubermensch that Buffalo is, but it still takes a pretty heavy snowfall to close the place. The kind of snowfall that clogs all the major roadways, doubles commuting times, and forces the morning news people to spend half of the show reading lists of school closings. In short, if DTW closes down, then most of the rest of southeast Michigan is shut down, too.
It’s rare that an airport will actually officially “close”.
Flight cancellations and delays usually happen because conditions are not acceptable according to the airline’s SOPs or the limitations of the specific aircraft that are using them.
Airports will report on the serviceability of various airport features in an effort to aid the airlines in making the decision as to come or go, but they do not usually prevent an airline from doing so if the airline deems it safe to do so.
There are many factors involved in making the decision. Runway surface condition is a consideration. Is the surface contaminated? How much of it? With what? What are the braking characteristics measured using friction measuring equipment and the experience of other pilots recently? What is the visibility? What are the atmospheric phenomenon? How long is the runway? How strong is the wind? What direction is the wind blowing relative to the direction of the runway(s)? Are the precision electronics that guide the aircraft to the runway working properly? What is the forecasted weather?
Once all of the decision making criteria are examined, they are compared to the minimum criteria that the airline and the manufacturer of the aircraft have established for safe operations. An ultimate decision is made to proceed or not. In marginal conditions, some flights will be able to go; some will not.
Obviously if there is 3 feet of snow covering the aprons and runways, no aircraft will move. However, an airport will usually only ban movements during very extreme situations.
Or an accident - an accident can close an airport to allow rescue equipment to move freely to and about the crash site.
Lightning can shut down ground crew operations, bringing everything to a halt. I got stuck in O’Hare one night due to this.