So you're thinking of planning a European vacation for the off season. November strikes your fancy. You are dazzled by the prospect that your vacation will be cheaper. You are worried about the weather, but are prepared for a lack of heat.
Let's stack up some pluses and minuses. Since you are excited and all, we'll start with the plusses.
Winter Vacation Pluses
It's cheaper. We've already mentioned that, but let's break it down to determine how much cheaper. You might get cheaper airfares, certainly you'll get cheaper fares than you'll find in the very high season. But these aren't the old days, the airlines have figured out how to cut back the supply of flights and sizes of planes so that fares don't have to dip precipitously from lack of winter demand. Hotels might cost less, but smaller (budget) hotels and B&Bs might charge extra for you to use the heat. Transportation, food, entrance tickets will all cost the same as they do in August. Your rental or lease car might cost the same, but you might have to pay extra for snow tires or chains--a requirement in some countries. Rail Passes will cost the same, but there may be money-saving specials and promotions to certain destinations available at the train station ticket window or through the web.
There will be fewer tourists. True. And there is likely to be fewer services available, especially in less populated destinations. All those college kids they hired as waiters at Chez Louis to speak English to tourists are back to school, so you might have to decide if you like cuisses de grenouille enough to attempt to pronounce the French phrase for frog's legs in front of a native speaker.
The (real) cultural activities have begun. Sure, on a steaming August afternoon someone might herd sweating tourists into a historic building in Vienna to listen to a Mozart pop concert given by music students, but as the weather gets cold the venues for professional art performances open up--and that's a real treat in the major cities. Besides, after a performance at the Vienna State Opera Hall you can slide over to a historic cafe for a drink that matters now, because you're chilly and the cafe is a warm and inviting place to hang out in winter--and it's worth lingering amongst the ghosts of literary Vienna for a while.
The light. Yes, the slanting light of winter and the brooding skies can make for some fine landscape photography. My best pictures are taken in November light. But of course there's less of it in late fall and winter. Europe is further north than you think; days can get very short by November. On November 1st the sun sets in Paris at 5:31. By the end of the month it's dark after 4:57 pm. Of course, if you prefer the dark, it can be a big plus.
Neither a Plus or a Minus, just different
Many inhabitants of European cities prefer eating what is available locally most times of the year. Thus summer food is different than winter food. Late fall is starting to get cool enough to get a cook thinking about simmering a stew for hours and hours over a hot stove. So while you might enjoy simply grilled meats and raw garden vegetables on the terrace in summer, long-cooked stews and root vegetables are what people are eating by the roaring fireplace as winter looms. If you allow yourself to go with the flow, you won't have any problems with fall and winter menus. I prefer cold-weather food. It allows chefs to shine.
And if you like truffles, the winter white truffle is best, and they start showing up in November--most of the truffle fairs and festivals are held then--a very good reason for a November vacation all by itself.
Negatives for a November Vacation
Short days; wind, rain, and snow. We've discussed these above. It's not hard to buy a heavier coat or a better umbrella anywhere in Europe, so don't worry. You might have to take a cab instead of walking, so there go some of those dollars you've saved on airfare.
Short business hours. Yes, many businesses close at dark. Tourist offices are a notable example. The time you take to "get things done" can be somewhat shorter as daylight hours shrink.
You'll have to pack large. Sweaters, jackets, boots and long sleeves take up way more room than typical summer far--and take far longer to dry if you're used to washing a few things in the hotel sink.
Winter Travel Tips and Resources
Late fall and winter is the time to visit large cities. European Cities are packed with attractions and have adequate public transportation. Cabs and the metro can get you around a big city. Renting an apartment with its own heat control can keep you warm and make you feel like you are part of things. Trains can relieve you of the dangerous bits of bad-weather driving. By the way, don't just think of trains as a way to move from city to city with your baggage, they can also take you to different places for a day trip visit. Base yourself in a big city, and think of places you can get to with a one hour train trip. Paris > Versailles for example. Or, if it's not raining in Burgundy, you could take the train to Dijon for the day.
If you are bothered by cold weather, but are limited to traveling in November, there are some fine places in the south to visit. The Greek island of Crete, for example, has daily highs averaging 68 degrees F and lows of 56 in November (source: Crete Travel Weather). Southern Portugal, Spain, Italy, France, And Greece can all be fine in November. My first trip to Europe spanned November. I enjoyed myself immensely. (Just start in the north, then head south--just like the birds.)
Tip: When searching for the future possibility of rain and the average temperatures, search for "climate" rather then weather. Searching for "crete historic climate november" should get you some charts of historic averages for the month of November.