No, they are strictly forbidden, and if you are found in possession of one you will be promptly executed.
Keep up the good work, loyal citizen
If you search the Family Friendly Storygames, you will find many wholesome tales of adorable fluffy animals, such as: Day of the Dog, Adventures of a Cute Cat, 4 Little Mice and The Brave Polar Bears, all of which have fur. I assume this is the kind of game you're looking for. ^_^