Yes, cats can get hay fever. Hay fever is also called allergic rhinitis (nasal allergies). Feline hay fever is caused by contact with environmental irritants and allergens. Pollen, dust and cigarette smoke are possible causes. Sometimes it might be a new carpet cleaner, deodorant powders or perhaps a new detergent for your laundry that might be the cause of nasal irritation. By the way ‘hayfever’ can be spelt as one or two words.

It is thought that “true nasal allergies” are uncommon and that most often periodic bouts of sneezing and a clear watery discharge from the nose by your cat are caused by reactions to irritants such as dust.
Therefore, “feline hay fever” is probably quite rare but it is on the list of possible cat illnesses. The treatment is obvious, namely to remove the cause of the irritation which will require a bit of research probably.
Like humans, I’m told that cats respond well to antihistamines and steroids. You must consult your veterinarian before administering these medicines.
Where there is chronic inflammation, it can lead to “an influx of lymphocytes into the nasal tissues”. Apparently, this is quite common in cats. Once again see a veterinarian who will probably prescribe anti-inflammatory medications to control it. In worst-case scenarios chronic inflammatory conditions may contribute to the most common form of nasal cancer in cats, nasal lymphoma.
RELATED: Cats with allergies becoming more common.
Update December 2022:

I decided to add some more information to this page to refresh it. The Knutsford Veterinary Surgery state that this is a seasonal allergy which it must be because it happens at that time of year when plants and grass or releasing pollen into the air. A cat’s immune system reacts to pollen as if it is a foreign invader. As the body tries to get rid of this “invader” there may be symptoms. Tree pollen occurs from March to mid-May while grass pollen occurs around mid-May until July.
The symptoms include an irritation of the skin. Hayfever in cats affects the skin more than the sinuses. This veterinary surgery says that hayfever can make cats quite unwell. The main signs include scratching of the skin. I guess this might lead to self-mutilation. People need to watch out for this very carefully because it can be quite damaging.
It may lead to sores and bald patches due to the constant itching. Sometimes the allergy may cause hair to fall out. A cat with hayfever may snore like humans. This would be caused by an inflamed throat.
There may be itchy and runny eyes, sensitive paws which may in turn cause the cat to lick her paws to alleviate the discomfort. In addition, there may be the usual sneezing, coughing and wheezing which may be particularly prevalent if the cat has asthma.
The treatment will be decided by veterinarian but might include daily antihistamines which reduces the cat’s immune response. Alternatively, or in addition cortisone, steroids or allergy injections may be prescribed. Finally, giving your cat a bath once a week will help to remove pollen from their coat which will in turn relieve itching.
There is no substitute, however, to removing the source of the hayfever. It probably can’t be removed completely unless a cat is kept indoors full-time and the indoor environment is vacuumed and/or there is an air filtration system inside the home. It may be helpful to brush a cat predisposed to hayfever in order to help remove the pollen from their coat. This can be done once a day.