The short answer: No.
The long answer: Though dogs can occasionally eat a few pieces of peanuts and cashews, walnuts are a big no-no for them. These large, hard-shelled nuts can block your dog’s airway, trigger gastrointestinal distress, and be the cause of toxic poisoning. Plus, moldy walnuts may contain tremorgenic mycotoxins that can lead to epilectic seizures or neurological symptoms. These may be found on the shell, and even after the walnuts are washed and cooked.
What to do if your dog accidentally eats walnuts: If your dog eats one piece that’s fallen off your hand or from the kitchen counter, he should be fine. Still, it’s best to keep an eye on him and monitor him for any unusual changes. Contact your vet if your canine displays signs of discomfort or tremorgenic poisoning. Symptoms for the latter include vomiting, fine tremors, loss of balance, and seizures.
If your dog consumes an unshelled walnut, call your vet immediately. Your dog may suffer from an impaction, with the shell getting stuck in his intestines and creating a block.
In summary: Skip the walnuts and just give your dog his usual treats. Even if they are packed with antioxidants and omega-3 fatty acids, walnuts can do more harm than good to your dog.