Changing feeds with the seasons is indeed advisable as their needs change, and the feeds you buy recommended for year-round fodder are often not taking into account the fact that the birds the feeds were initially developed for are often in caged and controlled environments. Free range birds, or those without climate controlled environments, will need adaptive diets.
I'm not sure about trying to put fat on them for winter, chickens retain heat more by using feathers as insulation, not fat, and burning resources to maintain higher body temperatures than mammals do.
During winter, lower protein is usually an issue, not a solution, even when you're talking about animals which have fat as well as a coat for insulation i.e. sheep commonly have low protein issues in winter and they're generally not low on fat.
Also many modern breeds do not lay down fat correctly, they tend to suffer internal buildup problems which can stop them from laying, and which offers them no warming advantage but rather plays havoc with their health, makes them predisposed to cardiovascular disease etc.
Higher energy food would probably help them more during winter, so perhaps adding some coarse grain mix or similar would be a good idea. It's really too variable between breeds, strains, feed types and brands, weather, environment etc for me to be able to give you concrete advice there. During winter, even though we're in the subtropics, we used pine boughs to insulate the main coops from wind and excess damp, just wove them among the chainlink mesh of the walls, which had all been open right up to under perch level. They loved it and I've never had problems with either weight loss or production loss in winter, but then again I don't live in a snowy place or rely on processed foods alone.
Best wishes.