Yes, if the aircraft is properly equipped and the pilot is IFR rated. There, certainly, could be conditions in which a plane can take off but the fog too dense to land. After all, you have to, at least at some point, see the runway to land.
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Every year, flights around the world suffer delays or even cancelations due to dense fog and low visibility. The risk of these conditions increases during the winter months when colder temperatures meet higher levels of humidity.
The type of weather that delays and cancels flights is called inclement weather. Inclement weather is categorized as thunderstorms, snowstorms, wind shear, icing, and fog. Any inclement weather is by far the most hazardous. This is the type of weather that causes the most cancellations and delays, not just rain.
Why can planes take off in the fog (we watched quite a few leaving) but are unable to land? A: The visibility requirement for takeoff is less than for landing.
Company policy dictates that low visibility landings must use the aircraft's automated systems that interact with the airport's instrument landing system. This is the array of metal poles at the end of a runway that generate a radio beam for aircraft to follow.
With this in mind, horizontal winds (also known as “crosswinds”) in excess of 30-35 kts (about 34-40 mph) are generally prohibitive of take-off and landing. As far as how this happens, it depends on where you are in flight.
Aerophobia is an extreme fear of flying. People with aerophobia might feel intense anxiety before or during a flight. This condition can interfere with your ability to travel for work or pleasure. If aerophobia is affecting your quality of life, talk to your healthcare provider.