According to EU law 261/2004
If an airline cancels a flight then you have the right to be scheduled onto another flight to your final destination, the airline has to provide assistance, and you have a right to compensation.
However, here we are talking about an exceptional situation. So the right to compensation will probably not exist, but the airline should still re-schedule or reroute you as soon as possible. But if an airport is shutdown for several days then this might take some time.
Also, although the airline has to provide you with assistance which includes accommodation, the reality is that if 100's of flights are cancelled that the hotels will also be full.
So I would suggest that you look into alternative arrangements yourself.
- As you are arriving by car, then consider to also leave by car (or train)
and then make alternative arrangements to get to your final
destination (which is why I assume you will fly)
- If you think that this is highly likely, then look at booking a
hotel yourself in advance. You can either:
- Book a cheap hotel rate and if not needed you lose the money
- Book a more expensive refundable hotel rate. And if not needed you
can cancel and get some or all of your money back (you often have to
cancel 24 - 48 hours in advance to get all the money back)