My cat as been having on and off stuffy nose and it sometimes sounds like loud snoring. However she has no discharge and eats and plays normally.

Upper respiratory infections, allergies, and minor issues with the throat or lungs can sometimes cause congestion or coughing/snoring sounds, however minor cases may resolve on their own with little symptoms. If your cat is still eating and drinking and acting normally, it may just be best to keep an eye on her and watch for any changes. If you do see symptoms such as wheezing, coughing, loss of appetite, fever, difficulty breathing or discharge from the eyes and nose, then scheduling a veterinary appointment for further care is best. If she stays normal, then bringing it up at your next vet checkup if still concerned is best so that your vet can make sure to examine those areas more thoroughly.

The most common cause of a snoring sound if your pet doesn't normally do this would be a respiratory infection - this can cause nasal congestion and a snoring sound when breathing or during sleep. Other possible causes would include a problem in the throat such as tracheal collapse or laryngeal paralysis, or a nasal tumor of some kind. If the problem seems to be improving and she is acting normal otherwise, you could continue to monitor her for the next few days to see if it resolves on its own. If the snoring continues, or if she develops any other symptoms, then I would recommend having her examined by a vet - he/she can do a thorough exam of her nose and throat, and may also do blood work or x-rays if needed to diagnose the problem.

Sneezing is most commonly a sign of an upper respiratory infection, although it can be related to allergies, foreign objects or even polyps or tumors in the nose. If the nasal passages are obstructed with mucous or inflamed then she may be breathing through her mouth because she can't breathe through her nose, however if you think she might be having difficulty breathing you should see a immediately. Otherwise I'd recommend making an appointment to see your vet when you're able for an exam and to determine what might be going on.