Yes, I find cardio makes a big difference.  I like doing a mix of high-intensity burst cardio (really clears out my nose and strengthens my muscular and respiratory systems, making them more resilient) and lower-intensity longer cardio (reduces my anxiety and increases my general health and happiness).  I find that if you have a dry nose, it's really important to moisturize well before exercise.  Even if you are breathing humid air, you are breathing so much of it so quickly that you can dry out your nose.  Also, be really careful about running, since we are that much more susceptible to falls or injury.  Do not run recklessly fast and DO NOT do it when you have aches and pains that have not gone away.  If you must run, I would still recommend mixing in some cardio that isn't hard on your joints (stepper, recumbent bike, etc).