I flew to Madeira on the 17th November 2012 and stayed five days. It was significantly warmer than the U.K. and some days I fell asleep by the pool. I didn't swim but there were people swimming. It was wonderful to get out of the British winter and the weather was just what we had hoped for.
Madeira was open for business. It is a major tourist destination in winter and I cannot remember anything that was closed. It is also a cruise destination and some days there were four cruise ships in bringing thousands of visitors.I had the impression that many visitors came here annually in the winter.
As for a destination I really enjoyed my stay. The island is beautiful and has copious numbers of hotels at every level. The food was not as good generally as you would have thought but we had some very good meals indeed.
There is a lot to do and public transport was well organised and readily available.
We didn't make it to a beach- this island is quite big and we left without having seen everything there was to see.
Combining this with Lisbon would be really interesting-but I'm not sure what the weather is like on the mainland October/November.
Similarly Barcelona/ Majorca- an interesting combination within the same country.
When I visited Majorca it was the beginning of May and again- significantly warmer than the U.K. We stayed in Fornalutx in the mountains which was quite gorgeous. We hired a car to drive around which was easy.
I'm not sure how many hotels and restaurants will be closed but I can tell you that sun-seekers in the winter tend to head further south in Europe.

Ditto what Frances said about Madeira - for years it's been one of the major "winter sun" destinations for northern Europeans. We've been there around 10 times in January/February, and everything is open throughout the year. There's a great selection of high-end hotels and nice restaurants and plenty to do and see, particularly if you rent a car and get up into the mountains, or along the spectacular coastline. There are no natural sandy beaches on Madeira, but there are a couple of facilities with imported sand (from North Africs believe it or not). All major hotels have swimming pools, often set in beautiful gardens with views of the ocean.

Let us know if you need any further tips/recommendations - Madeira would be an excellent choice for a honeymoon.

Thanks to both of you! We are still deciding but I'll be back with an update soon.