I, too, get worse mpg in the winter on my 05 gs1200. I mostly suspect that the fuel program for the bike takes the temp and decides that the cool weather requires a certain level of enrichment not needed in warmer temps. And there is nothing the owner can do about that which would seem worthwhile. Use a thermostat rated for 200 as opposed to 180 degrees? The cardboard over the radiator might work if the rider was willing to make the hole adjustable and remember to remove it before the engine overheated on warm days? Paying attention to the bike's engine temp gauge would be a useful skill. I doubt that warmer plugs would help if the bike will start on reg temp plugs. That might work on some air cooled bikes. But I have my doubts if the engine is liquid cooled? The bike warms up to operating temp or it doesn't. MY GS temp gauge never varies by so much as one bar regardless of ambient temp after the bike warms up. Granted, I let the bike idle a little more in winter so that the heated grips get started before I have to get moving. If you are running electric gear and slowly commuting, maybe the bike uses more fuel to keep the voltage up?
My suspected guess is ambient 55F is where my enrichment hits. Above that, I get 240/tank. Below that I am lucky to get 210. As I get down to 20F, I might get 180-190 out of a tank at commuter speeds.
For every bit of automated/programmed stuff by the manufacturer, there is a trade off. Stuff that works perfectly in the state of the manufacturer works less so everywhere else. As an example: HD's auto-cancelling turn signal program works damn good here. My GS system nearly kills me several times per week. It either quit way too soon or stays on way too late and it rarely gets close most of the time. Makes one wonder how good the rest of the computer programming is? My first hint of things to come was noting that the clock did not keep good time. A $3 timex digital from the discount bin at the local drugstore out performed the factory unit by whole minutes over 6 months.