Unless your dog has a food allergy to the meat, an occasional nibble or two of cooked venison should not pose a serious hazard for a healthy dog, Tamara. However, it is important to keep in mind that any food that is not part of your pet's normal diet—especially those high in fat, such as roasted meats—can cause gastrointestinal upset. The consumption of large amounts of fatty foods may also lead to pancreatitis, a serious inflammatory condition of the pancreas.
The bottom line? If you decide to offer your dog a treat of cooked venison, please do so only on occasion, and in small amounts.