henry,
I would also suggest leaving the Cinque Terre for another time, at a more favorable time of year. In late November many of the tourist businesses will be shutting down for the season, so your choice of hotels, restaurants, etc. may be rather "limited". In addition, as you noted the weather may be miserable and your experience there may not be the most pleasant. There have already been some severe winter storms in Liguria and damage has occurred. The first photo in this report provides an example - https://www.thelocal.it/20181031/veneto-and-liguria-count-the-cost-of-storms-and-flooding .
Regarding the trails, the popular Sentiero Azzurro trails will probably "officially" be closed, although that may not be monitored. It's probably not a good idea to hike those in wet weather, as some parts could be muddy and a bit treacherous. Only two of the four segments of those trails have been open for the last few years, so hiking on those would be limited anyway.
If you're going to be in Florence for a few days and the weather is good, you could take a day trip to the Cinque Terre just to have a look at the five towns and get some ideas for a future (longer) visit.