You're not going to find many local vegetables in Vermont in the winter. True, we're south of Paris, but the ground is frequently under 50 centimeters of snow and ice, with occasionally nighttime lows of -20°C or below during cold snaps.
Under these conditions, about the only winter vegetables that you can grow are mâche and maybe claytonia. Basically, you plant them in the fall, and allow them to overwinter in cold frames, or in hoop houses with row covers and a few degrees of artificial heat. You can't harvest the claytonia until the temperature goes above freezing, or it will wilt. The mâche can be harvested frozen and then thawed out. And it's a great salad green—tasty and attractive, without being bitter. I've grown both, and it was fun, but not terribly practical.
To read about some really epic winter farming in the northern US, check out Four Season Harvest: http://www.amazon.com/Four-Season-Harvest-Organic-Vegetables... Eliot Coleman has thought longer and deeper about this than just about anyone around here, and his book tends to suck geeks right in.
But even Eliot Coleman has given up on January farming in northern New England. He can do it, and he can make money, but he prefers selling tons of salad greens and sweet baby carrots for the December holidays, and then spending January vacationing someplace warm. Mâche is pretty awesome, but it's not enough by itself.
It's not easy to make a decent living of a tiny farm, but some people have done it. Most of them target higher-end products and direct-to-customer sales. For example, Eliot Coleman had a 5-acre farm on the coast of Maine that apparently did fairly well selling fresh local vegetables during the fall and spring for many years. His book is excellent and fascinating: https://www.amazon.com/Four-Season-Harvest-Organic-Vegetable... One of his big staple crops was really good carrots during fall months, because frost makes carrots sweeter, and if you don't use machines to harvest them, it's possible to grow tastier varieties.
There are also some very tiny Vermont farms that produce gourmet cheese. This obviously adds a huge amount of value to their milk production.
So in general, you're right. But it actually possible to make a living selling luxury products to foodies. The stereotypical farmer in this market is somebody who retired young from Wall Street, and who has fairly impressive business and marketing skills.