With beets, I tend to harvest the
roots and greens together. You can take leaves here and there to eat without killing the plant/root, but understand that when you do this (or take onion tops, for another example), you are taking the part of the plant that collects the
energy put into making the beetroot, so you will end up with a smaller
root at the end than if you hadn't taken the leaves. You can harvest beets at any size - what I tend to do is seed pretty close together, do a first thinning like I would with carrots or parsnips to give the roots some room to grow, and then thin out the more crowded spots over the season, getting small beets at first and giving their brothers and sisters more room to get big. By the end of the season, I usually have some pretty decent beetroots, if the rodents don't get them first!
And up here in the north, I'm pretty sure you can't overwinter beets - they sit too far on top of the soil. Carrots and parsnips can survive in the ground (though I'm planning to mulch mine well before the ground freezes), and parsnips get sweeter when left in the ground overwinter.