You will not find an objectively non-nutritious cuisine, as people would die.
But I have an answer valid at least for part of the year.
The Iroquois / Huron in Canada did not have a comfortable way of cooking or heating their tents. The cold required them to have a fire, but they could not have good ventilation or smoke management, and the French Jesuits who went there had great difficulty adapting to the smoke: not just they had respiratory or eye illnesses due to the constant smoke, but all food would be tasteless as the sense of smell was compromised. And the food in winter was already very limited - dying from hunger was quite common among the Indians - they would eat whatever they could, even tasteless barely-edible frozen roots from plants or small animals which they would never even touch in summer.
The Jesuits were surprised that the Indians themselves were more resilient, of course, but not completely. In terms of health, serious respiratory issues were common, even causing early death. And in terms of food taste (and abundance), the Indians themselves quite preferred (as they sang, complained and dreamt about) the summer or larger villages with better accommodations where the smoke issue was not so important.
So, at the end we concluded that summer is easier than Canadian winter (duh!)... and when food is scarce you eat anything edible (duh!^2)... Probably you can find similar issues in primitive civilizations in colder or drier climates...
just to be more specific about food/hunger in winter, they depended on hunting herds of large animals (moose?), which migrated for winter, but could take different paths. When they missed the path of the herds, they knew that there would be not much food for months and some of them would die.
(this info is in a Jesuit book about the Canadian missions. I do not remember the name)