The ongoing COVID-19 pandemic caused by infection with SARS-CoV-2 has created an urgent need for animal models to enable study of basic infection and disease mechanisms and for development of vaccines, therapeutics, and diagnostics. Most research on animal models for COVID-19 has been directed towards rodents, transgenic rodents and non-human primates. The primary focus has been on the angiotensin-converting enzyme 2 (ACE2) which is a host cell receptor for SARS-CoV-2. Among investigated species, irrespective of ACE2 spike protein binding, only mild (or no) disease has occurred following infection with SARS-CoV-2, suggesting that ACE2 may be necessary for infection but is not sufficient to determine the outcome of infection. The common trait of all species investigated as COVID models is their health status prior to virus challenge. In contrast, the vast majority of severe COVID-19 cases occur in people with chronic comorbidities such as diabetes, obesity and/or cardiovascular disease. Healthy pigs express ACE2 protein that binds the viral spike protein but they are not susceptible to infection with SARS-CoV-2. However, certain pig breeds, such as the Ossabaw pig, can reproducibly be made obese and show most aspects of the metabolic syndrome, thus resembling the more than 80% of the critically ill COVID-19 patients admitted to hospitals. We urge considering infection with porcine respiratory coronavirus of metabolic syndrome pigs, such as the obese Ossabaw pig, as a highly relevant animal model of severe COVID-19.