I played off the grid already and it is a new favourite style of mine because it is extremely challenging. My sims walked around at least a little or a lot tense because they were cold (even with a fireplace in the house), they did not feel completely clean, and their fun levels dropped fast.
Cooking is not difficult: if you buy the old-fashioned stove you can cook with gas and make single serving dishes of eggs with toast and grilled cheese. You can get cold food and drinks from the OR cooler and grill various foods on the outdoor barbecues, and if you have the old-fashioned fridge and a counter, you can also make garden salad, fruit salad and sandwiches (under Quick Meal); it can also act as a pantry to store fruits and vegetables.
No baths are possible and showers give an uncomfortable tepid moodlet and a sense of not being fully clean. (I imagine living by the ocean will make this aspect easier because sims can always swim). As for the fun need, my sims will all be forced to become musicians, artists and bookworms just to make them able to be happy.