The common cold is much more frequent in winter months, a trend that is seen in all countries of the Northern Hemisphere. Rhinovirus, the most common cause, shows peaks of activity in late autumn and early spring.
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So far there has no generally accepted explanation for the observed seasonality of the common cold.

Source : UK NHS Clinical Knowledge Summaries (archived)

Despite intensive research projects in many countries over several decades, the cause of the Winter peak figures for the Common Cold are still not known.

There have been many suggestions for explanations, One being that the human immune system is somehow debilitated on exposure to low temperatures, making it easier for the virus to 'take hold'.

However, a set of experiments carried out in 2002 at the Common Cold Centre, Cardiff School of Biosciences, UK, tested the idea by deliberately exposing volunteers to the cold virus, then providing low temperature accommodation for half the participants. There was no difference in the development of colds between the two groups.

There is a widely held belief that acute viral respiratory infections are the result of a "chill" and that the onset of a respiratory infection such as the common cold is often associated with acute cooling of the body surface, especially as the result of wet clothes and hair. However, experiments involving inoculation of common cold viruses into the nose, and periods of cold exposure, have failed to demonstrate any effect of cold exposure on susceptibility to infection with common cold viruses.

See Acute cooling of the body surface and the common cold Rhinology, 2002 Sep;40(3):109-14.

Another theory holds that the seasonal differences are largely due ro behavioural and social factors. People tend to congregate indoors - with poorer ventilation - when the weather is cold. This makes person-to-person airborne transmission of the virus more likely. (Recent experiences with the COVID-19 epidemic have shown that indoor air filtration systems can dramatically cut down transmission rates)

A third idea is that there could be some changes in the physiology of the respiratory system when breathing cold air. For example the Mucociliary Clearanceplugin-autotooltip__plain plugin-autotooltip_bigMucociliary Clearance

"Mucociliary clearance is the first line of defense of the mammalian respiratory system. The mucociliary system consists of two major parts: mucus and cilia. Mucus is a thin fluid layer that coats the lung airway; cilia are hair-like organelles protruding from the cell surface and bathed in the mucus. With breathing, the mammalian respiratory tract is constantly in contact with particles in the air that could contain potentially infectious microorganisms or toxic substanc… system could be less efficient.