the Cinque Terre in December

Different from many destination, there is not a lot to do indoors the Cinque Terre in typical December weather for that area, since the CT is a place to do things outdoors, such as hiking between villages - activities where the weather affects the quality of your experience and enjoyment. Since most travelers go to the CT to enjoy outdoor activities, many tourist activities and services are closed or curtailed in December. So yes, your original suspicion is correct: that December is not a good time to visit the CT, and very few people posting here seem to go in December. Most people posting here seem to visit the CT between about March - October, and in my opinion the best months for weather and crowds would be April, May, and September.

Gayle, as Kent mentioned, that's probably not the best time to visit the Cinque Terre. The weather could be "inclement" and also as you discovered many places close, especially during December and January. During bad weather, some of the trails may be closed due to "washouts" or hazardous conditions. What time during December will you be travelling? You're more likely to find accommodations in Monterosso, as it's the largest of the five villages, however during Christmas some of those may be closed also. ¶ Have you considered staying in Varenna on Lago di Como instead? Good luck!

I wanted to add that a number of travelers go to northern Italy destinations in the winter, fewer crowds and lower costs - but most of them are aware of typical winter weather there and plan their trips so they're in areas where there are things to do indoors. The CT is mainly a place to do outdoor things. Monterosso is more of a "resort" area than the other 4 villages.

I recommend staying in Santa Marguerita or La Spezia rather than in one of the 5 towns. These are larger cities and should have lodging all year. I probably would not visit the CT in December.

The question is what would you do in CT during December? Very likely, the trails would be closed and not accessible for hiking. Very likely, there water will be choppy and no boats can operate. Yes, you still will be able to find accommodation. Yes, you still will be able to find restaurants. And you can spend some VERY relaxing days there, doing nothing which in itself can be nice too. But you can do all that in other places in Northern Italy AND enjoy additional interesting and/or relaxing activities.