On Earth, there are crops that are planted before winter, and are left to germinate throughout winter. They then grow in spring and are harvested in the summer. On Planetos, these crops have adapted to survive. For instance, in Act One: Chapter Three, Michael plants barley and turnips and garlic for the winter. While these plants on Earth are capable of germinating in winter, they don't grow. In contrast, on Planetos, they do grow if certain conditions are met.
They can't be buried under snow once they have begun to sprout for very long, or they stop growing. They do not have as good of yields as the summer varieties, and typically require more space. Specifically, the barley cannot be planted close together. Instead the seeds are more spread out and there is room between them. Typically, they also have wide rows between them (for reference, a bit wider than crops like potatoes) so that snow can be cleared easier. The space between each plant in a row has quite a bit of space, but not enough to walk without brushing up against them, but more than they would usually require. The barley also has a much shorter stalk, and less grain per stalk. The barley is also unique, in that it will grow throughout winter, but will not fully mature until it receives a signal. By fully mature, I mean that the stalk will grow to its maximum length, and then once the signal is received it begins to grow the grain. This signal is a biological signal that sweeps down from the North on the air (like a pollen). This signal indicates that spring is coming. Some animals and plants can receive this signal and understand what it means.
Farmers can use this signal as a timeframe and will then plant other crops (like turnips or garlic). These plants are much more resistant to the cold and aren't killed by frost. This allows a farmer to technically grow food over a winter, but he won't be able to eat it until spring. This alleviates some hunger near the end of winter and into spring but does not help during the height of winter. However, some breeds of grass and fodder plants do grow in the winter, however very slowly. They must be unburied and have some sunlight to grow, but they will not be killed if buried.