You know I'm going to say it, don't you? The most obvious thing for me, and hopefully for you too, is to swim.
If you haven't started swimming, I enthusiastically encourage you to start. Swimming is an excellent, comprehensive form of exercise, regardless of whether you have RA or not!
When I first began swimming in earnest at the age of fourteen by enrolling in a competitive swim club, little did I know that this would be the one exercise that has carried me through the decades of flares, surgeries and pain.
When you are so sore and stiff and feel less than fluid in your movements, the weightless you experience in the water gives you back that all-important sensation of mobility. If your reason for not going in the water is because you are cold, pick up the pace and focus on the exercises and movements, as opposed to how cold you feel. You'll soon warm up.
Dependent upon your degree of comfort and skills in the water, you can work on endurance, flexibility, mobility, range of motion and strength. Don't forget to simply float at the end and rejoice in that feeling of letting-go.