My in laws live just outside of Klamath Falls. I'm not sure what cycling clubs might be in the area, but I can tell you there are loads of good cycling routes in the area and good mountain biking nearby. It hardly ever snows enough to stick on the roads in K-Falls, but it can get extremely cold. The OC&E rails to trails runs right through town and is an good option for a winter ride when you want to stay off the main roads. The locals often don't yield the right of way to cyclists, especially in the off season, so keep your guard up. There will be days you will not want to attempt to ride, but there are often winter days where you can make it work.
Try asking at
Hutch's Bicycles, they should know what clubs are in the area. You also might want to think about joining a gym for those times you just can't get out and ride. Many gyms have fantastic classes that end up having a social aspect that might be just what you're looking for.
If you're wanting to try a new sport, look into cross country skiing. There are many excellent places to ski within a 45 minute drive including Crater Lake.
I always look forward to visiting my in-laws although I spend more time off exploring the country than actually visiting!