Brachycephalic breeds is something that one would probably think of first.
Their anatomy leads to challenges during intubation, and there is a higher risk of airway obstruction. Special measures need to be take both during induction and during recovery. Close monitoring, and potential oxygen supplementation, during recovery from anesthesia are crucial.
With toy breeds, just their size creates its own special challenges.
Placing IV catheters is challenging simply because of their tiny blood vessels in their tiny bodies. Small breeds are also more susceptible to hypothermia. Even anesthetic monitoring itself can be challenging.
Greyhounds have documented breed-specific sensitivity to, and prolonged recovery from some anesthetic drugs.
Herding breeds might have prolonged effects of some anesthetic drugs.
Their genetic mutation can lead to toxicity of some drugs, well-known example of which is ivermectin. The same mutation can result in prolonged or excessive sedation from some anesthetic drugs.
Giant breeds require lower drug dosages.
Giant breeds often do not need the same mg to kg of body weight doses as smaller breeds to get equal sedation. I wonder if that was the reason why JD was groggy well up to midnight of the day he had his mast cell tumor removed.
Also, because of their shorter life expectancies, they become geriatric relatively early, which also calls for conservative drug dosing.
Is your vet aware of these breed-specific challenges?
Canine Breed-Specific Considerations for Anesthesia