The best way to store the green tomato is on the countertop away from direct sunlight, with the stem end up. For the best taste you should use the tomato within 1 week once ripe. The tomato may keep a little longer depending on how ripe the tomato was when it was picked. Tomatoes should not be refrigerated until you cut them, as this affects their taste. Unless you can the tomatoes once they are ripe, you likely can’t keep them all winter.
The best way to store apples is to refrigerate them in a plastic bag away from strong-odored foods. Again for the best taste, you should use the apples within three weeks although apples may stay fresh for longer periods of time stored in the refrigerator. Chances are that they won’t last all winter either. Your best bet might be to prepare them in such a way that you can use them later in a recipe. For example, can the apples and then use them in an apple crisp dessert later in the winter.