Get great at climbing hills
I would suggest a three-pronged attack to make you a better climber. Firstly use the bad weather months to develop strength not only in your specific climbing muscles (the quads by performing squats) but in your core too. Secondly, shed excess weight (this should happen naturally as you gradually increase your training volume) thereby improving your power to weight ratio, and thirdly, when finally spring arrives, get out on your bike and climb.
Lay the foundations first by spending 4-6 weeks (depending on your training history) including several modest climbs (of 3-6% incline) into your rides. These are typically hills which are not so steep as to force you out of your saddle. Stay seated to strengthen your hip flexors and increase the length of a hill climb to 6-8 mins if possible. Then move on to steeper, shorter climbs and work harder to develop more strength. Finally, you can turn your strength into power by including maximal efforts in the last 20m of a climb.
When climbing stay relaxed, but engage your core, keep your back straight, and rest your hands comfortably on the bar tops. Sitting tall rather than being hunched will make more space for your lungs to expand and allow you to get more oxygen into your body. And on moderate climbs, still aim to keep your cadence at around 90 rpm.