My 2005 standard GS (not the Adventure version), both in the owner's manual and on the handy guide under the left-hand side plastic cover, clearly calls for 2.2 bar or 32 psi (front) and and 2.5 bar or 36 psi (rear) for solo riding (no luggage or pillion). Suspecting that BMW development engineers might have put a bit of effort into this I respect the suggested figures and stick to them. The bike has always had excellent feel using the recommended pressures, irrespective of tyre choice. One time after returning from a trip with the missus I forgot to lower the pressures to the solo recommendation and the reduced feel was immediately noticeable and much more 'wooden'. For the past two years I've been using the Avon Azarro/Storm combo at the recommended pressures. They give superb grip and feel, rain or shine, all year round. Give your tyres a few miles to warm up.
Soften up the suspension a bit. Unless you're a heavyweight rider I'd consider backing the front spring preload right off. Although cooler weather can make suspension stiff in the first mile or so you really just want the rear set up properly for your weight (preload) and rebound. The standard rebound setting is 1 1/2 turns out and your ideal setting won't be far off that. If you're running the stock rear shock the preload adjuster can lose its range of adjustment over time but it's easy to fix.
When it's cold we tend to ride more tense. Any arm or shoulder tension goes straight into the handlebars with immediate effect on steering and handling. Stay as relaxed as possible. Do the 'flappy bird' thing and keep your elbows down. There is no substitute for good riding gear. You're got to stay warm and dry to stay loose. BMW's Phase Change thermal underwear is the next best thing to heated clothing.
If you haven't taken advanced rider training give it serious consideration. There are plenty of options and they're all good. You'll learn to ride smoother and more relaxed and better anticipate hazards, winter or summer.