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We live just over the hills from there on the Bagni Di Lucca side, and the winters can be quite cold, this year we had a low of -12C and get snow of some sort every winter. There can also be lots of rain and wind (it is the mountains after all) but there are lots of Crisp, dry winter days as well. Be advised that you are required to carry Snow Chains in your car from November to April, and also Winter Tyres are advisable as not all the roads get gritted straight away. Having said all this do not be put off as everybody copes as this is the expected conditions for that time of year, unlike the UK were half inch of snow brings the country to it's knees.

It's unlikely that the cold will do any harm to your house itself - obviously you'll need to take precautions with things like central heating radiators and boilers, maybe even some water pipes if they are exposed anywhere - but traditional �������� houses are heavy and solid enough to resist almost anything the weather can come up with. Selling an olive grove depends really on where it is: if it has a good road to it and is near a village you might find someone wishing to take it on, but it's basically a hobby level activity (unless you are a farmer with zillions of hectares and heavily mechanised). It won't fetch much, and I'd think carefully about selling it if it adds to the aesthetic appeal of your house. 

Also worth considering is how you heat the house in the winter, a low of -12c is unusual for us in Marche at 420mtrs, and away from the mountains , but it still gets cold, and last winter we had very heavy snow, worst months seem January/Feb. We have about 70 olive trees and I do wonder sometimes as we are both retired how we will continue to manage them....but the oil is wonderful, so as my neighbours in their late 70s are still harvesting theirs we will keep going. (or get them to do it for us!). But seriously there are always people who will swap olive oil for the labour of picking, so I should not worry too much.