Good morning, As I can see here that you love your mother and you are panicking a lot regarding her medical condition. You may have searched in internet regarding the disease and may have read some information, which I would suggest not to do this in future as this will panic you, instead you can directly visit a doctor and discuss regarding the condition.
Coming to Rheumatoid Arthritis it is an inflammatory disease, but mainly attacks the joints in the body. So your mother will experience pain in joints, restriction in movements of the joint and in a long run or severe cases deformity may be formed.
There is a treatment for this disease but will not completely cure the cure the disease but checks the progression of the disease.
As you are panicking that it will affect the heat, lungs yes it will but only when it is very severe, so for that no need to panic what you can do is check your mother for RA factor and other Routine investigation along with chest xray. As this will give a picture of her health profile.
Next Steps
Can keep warm compress on joints when paining.
Avoid too much exposure to cold weather.