We are starting to plan a vacation late next year and want to go to Cornwall however I wonder what the weather is that time of year and as it is off season will most tourist things be open?
Weather - with the greatest of respect, who knows? This extremely cold snowy winter is unusual but we have had dodgy weather for several years now. Generally Cornwall is warmer than most of the UK but also very wet in late autumn. As for what's open, most of the National Trust is either closed or closing. What attractions are you interested in? Many will have websites and a little googling may give the results you need. For specifics that's what I would do.
When I lived in the UK in the 1990's, the first trip I took away from London was to Cornwall in early December. The weather wasn't a problem: Windbreakers and sweaters. The biggest problem was forgetting how early it got dark. If you're driving, plan on finding your hotel or b&b by 5pm.. Winter weather in the UK is fickle. But, if anyplace is going to stay "fair and mild" it's bound to be the southernmost portion of the island.
Most towns in Cornwall are small- so after dark not much to do, unless you stay in one of the larger towns. And it gets dark early. The Cornish countryside is great, but probably better seen in Summer