Yes, that can happen. Typically not because of snow on the ground: airports have the necessary equipment to remove that. More because of heavy snow storms that may make landing or taking off impossible for a while.
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“In most cases, snow falling below the base of a cloud deck is not an icing threat. Snow tends to just blow around the surfaces and does not adhere to the airframe. Flying through heavy snow at slightly warmer temperatures can cause a blockage of the induction system on some aircraft.
Like on public roads, airports do use regular snow plow trucks, but on top of that, there also brush the runway to make sure that every piece of snow is removed. After the Runway is clear, the airplanes need special treatment.
However, winter weather's impact on airport operations, particularly when combined with peak holiday travel, can create frequent, highly-visible disruptions. Snow, black ice, and slush are just a few of the winter conditions that create difficulties during take-offs and landings, as well as for low-altitude flights.
Just because there is winter weather outside, it doesn't mean that planes will suddenly stop flying. As we've discussed above, snow, ice, and bad weather do not hinder a flight. It remains safe to fly as long as precautious and pilot training are both up to date.
Crosswinds greater than 50-60 km/h may cause airlines to delay or cancel flights. Even lower gusts can trigger flight delays or cancellations if the runways are wet or icy, as stiff winds can reduce a plane's ability to brake on the runway.
Commercial jet aircraft fly in the lower stratosphere to avoid turbulence and increased atmospheric drag, which are common in the troposphere below. Air is roughly a thousand times thinner at the top of the stratosphere than it is at sea level. The stratosphere is very dry air, containing little water vapor.
When an aircraft experiences turbulence, the plane can drop or change altitude suddenly. This is why pilots always caution passengers to buckle up and stay seated when they are experiencing flight turbulence. The sudden movements put passengers at risk.
At times like this, pilots will slow to a designated “turbulence penetration speed” to ensure high-speed buffet protection (don't ask) and prevent damage to the airframe. We can also request higher or lower altitudes, or ask for a revised routing.