Introduction:
Convection is a mode of heat transfer that occurs due to the movement of a fluid. It involves the transfer of heat energy through the bulk movement of molecules within a fluid such as air or water. Convection can occur in various scenarios, but not all phenomena are related to convection.

Explanation:
Let's analyze each option to determine which one is not related to convection:

a) In winter metallic handles appear colder than wooden door:
This phenomenon is not related to convection. It is actually related to the thermal conductivity of different materials. Metals, such as metallic handles, have higher thermal conductivity compared to wood. Therefore, when touched, metallic handles conduct heat away from our hands more rapidly than wooden doors, making them feel colder.

b) Maintaining comfortable room temperature in cold countries:
This phenomenon is related to convection. In cold countries, the temperature inside a room can be maintained at a comfortable level by using heating systems such as radiators or heaters. These devices heat the air in the room, causing it to expand and rise. As the warm air rises, it creates a convection current, distributing the heat throughout the room.

c) Formation of trade winds:
This phenomenon is related to convection. Trade winds are a pattern of prevailing winds that blow from east to west in the equatorial region. They are formed due to the convectional heating of air near the equator. The intense solar radiation at the equator heats the air, causing it to expand and rise. As the air rises, it creates a low-pressure zone, and the cooler air from higher latitudes flows in to replace it, resulting in the formation of trade winds.

d) Formation of land and sea breezes:
This phenomenon is related to convection. Land and sea breezes are local winds that occur near coastal areas. During the day, the land heats up more quickly than the sea. The warm air over the land rises, creating a low-pressure zone, and the cooler air from the sea flows in to replace it, resulting in the formation of a sea breeze. At night, the land cools down more rapidly than the sea, causing the warm air to rise over the sea and the cooler air from the land to flow in, resulting in the formation of a land breeze.

Conclusion:
Out of the given options, the phenomenon of metallic handles appearing colder than wooden doors in winter is not related to convection. It is primarily influenced by the thermal conductivity of different materials. Convection, on the other hand, is involved in maintaining room temperature, formation of trade winds, and land and sea breezes.