This isn't really a complete answer but I can't fit it into a comment.
I've found that there is a large body of literature on seasonality of melatonin levels in various vertebrates, particularly livestock, because of its interaction with breeding patterns. Similar studies in humans are however, difficult to find, but the review paper cited below looks at a link between seasonal variations in melatonin levels and seasonal variations in immune system functions. It cites a few references that might be worth following up.
Srinivasan, V. et al. (2008) Immunomodulation by melatonin: Its significance for seasonally occurring diseases. Neuroimmunomodulation 15: 93-101 DOI: 10.1159/000148191
Melatonin is not only synthesized by the pineal gland but also in many other organs and tissues of the body, particularly by lymphoid organs such as the bone marrow, thymus and lymphocytes. Melatonin participates in various functions of the body, among which its immunomodulatory role has assumed considerable significance in recent years. Melatonin has been shown to be involved in the regulation of both cellular and humoral immunity. Melatonin not only stimulates the production of natural killer cells, monocytes and leukocytes, but also alters the balance of T helper (Th)-1 and Th-2 cells mainly towards Th-1 responses and increas- es the production of relevant cytokines such as interleukin (IL)-2, IL-6, IL-12 and interferon-γ. The regulatory function of melatonin on immune mechanisms is seasonally dependent. This fact may in part account for the cyclic pattern of symptom expression shown by certain infectious diseases, which become more pronounced at particular times of the year. Moreover, melatonin-induced seasonal changes in immune function have also been implicated in the pathogenesis of seasonal affective disorder and rheumatoid arthritis. The clinical significance of the seasonally changing immunomodulatory role of melatonin is discussed in this review.