A Vetter fairing and the lowers would help getting some heat to the airbox.
You have NO IDEA how well this works - unless you've done it!

I have both, and you are absolutely right. In cold weather I screw on the Lowers and the bike runs better than in the summer, every time. Once the temps get above 80 degrees or so, the carbs can boil [modern ethanol-laced] fuel in the carbs with the Lowers aboard, though, not so good. So, the Lowers come off in Spring.