I think the question was If insulin does not cause weight gain through the year, then what changes to make us put on fat in the winter?
For a start, in the older times, we became less active in the winter months, With home gyms and Pelatons that is perhaps not so important.
Secondly, with modern food storage and all round food availabiliy (perhaps not so well provided post covid?) then we no longer need to lay in fat for the winter. Note that the fat gain is in advance of winter and is triggered by Harvest Home and the pickling / jam making season. But many mamals overeat in this autumn so as to be able to reduce activity when the cold days come. Hedgehogs bears squirrels prepare for this, humans lay up food in storage and preserved foods instead. There is no specifiec mechanism involved apart from a tendancy to over eat the goodies from summer, intake of more frutose than usual (again not necessarily so in modern society) and slowing down the metabolism.
Those of us of older disposition may remember our grand parents doing the post harvet rituals of pickling, curing ham and bacon, drying fish and making fruit cakes. We may also remember Olive Oil being very expensive and not a common salad dressing. Salads used to have mainly vinegar only. Tallow and cod liver oils were not very helpful for this purpose and seed oils had not been invented in my early years. Sadly cod liver oil was plentiful YUK.
Nature controlled our fructose intake naturally by making these food sources seasonal. Mankind has resolved this problem and now we cn gorge on fruit all year round, thus potentially feeding the obesity crisis that we appear to be suffering now.