Another piece to the puzzle is how do fatty acids fit into this theory. First, we know that as the omega-6 to omega-3 ratio has gotten worse in the U.S. over the years, people's health has declined. The next question is how does this relate to the different seasons.
Prompted by an earlier commenter, I found this fantastic article by Susan Allport. She discusses how omega-3s are "spring fats" and omega-6 are "fall fats". Spring fats cause us to lose weight in preparation for mating season, while fall fats tell us to stock body fat for the upcoming winter. There are additional followup articles at Susan's website.
This idea about spring fats and fall fats leads to other connections. First, you can look at nuts, which are an autumn/winter food. Over at the Paleo Diet website, this table show the omega-6 to omega-3 ratio for various nuts. Almost all the nuts listed have a very high n-6/n-3 ratio. Is this just a coincidence that these fall foods have a high ratio? I doubt it. Most likely, the changing fat ratio in these fall/winter foods signals the body to store fat.
I don't want to make it sound like nuts cause obesity. In studies, nut consumption may produce only produce a small weight gain. The normal cycle of the winter metabolism probably only produces slight weight gain. It is the idea of a modern person being in a continual winter mode that could ultimately lead to obesity.
The next question is how available are omega-3s during the summer months. Another graph from the Paleo Diet website shows the changing fat levels of wild game over the season:
The omega-3 fats (polyunsaturated) are not that prevalent in the summer months. However, if you believe that seafood played a large role in the Paleolithic diet, then you have your answer as to why omega-3s are a summer food. Fatty fish with their high omega-3 content are most prevalent in the summer months.
There is one other way to tell if omega-3 fats are a summer food. You could find out if the consumption of omega-3s gives skin protection from the summer sun. As it turns out, they do. This document shows how omega-3 fats provide skin protection from "the inside out" in terms of UV radiation.
Overall, this shows how fatty acids may play a role in shifting the metabolism into winter mode. The modern diet tends to be low in omega-3s and high in omega-6s. Refined foods and junk food often contain vegetable oils, which have high levels of omega-6 fats. Shifting towards "spring fats" like omega-3s may facilitate weight loss.