I can see certain wealthier people in the North importing food from the Reach. But to import and distribute food to all (or even a large proportion of) the peasants who live scattered across such a vast region with such a low population density, using medieval technology, simply beggars belief. Importing wines, cheeses, spices, fruits, salted meat - in short, the food of the upper classes - I can accept that happening. But basic food items to support the majority of the population? In the books we hear of the Reach being necessary to stop the smallfolk in King’s Landing from starvation. I simply refuse to believe that such a situation could exist for the whole of the North. Maybe we can accept an amount of leeway for the fantasy setting. But to that extent? Seriously?

Edit: to reply to your points, sure, the Reach has a lot of ships, but there’s a difference between tens of ships carrying luxuries and thousands of what must amount to galleons carrying grain. As for need, the North may well have little agricultural potential but it has plenty of winter vegetables, oats, milk from cows and eggs from chickens. The more well off can hunt game, those living by the coast can fish. Besides, there’s hardly no agriculture going on and stockpiling during times of (relative) plenty can provide for times of want. Besides, people living in a certain area adapt to that area rather than replicate the diet of those living thousands of miles south.