I’m afraid that purchasing insurance at this stage in the hope of it offering cover against disruption is not going to help. If you look at the terms and conditions of the policy, it will specifically exclude claims for disruption when that disruption has already commenced, or could reasonably have been expected to commence, at the time of policy purchase.
Your airline does, however, have an EU ‘duty of care’ to look after you until such time as they can fly you themselves, or deliver an alternative. Broadly, this amounts to overnight accommodation and three daily meals.
Different carriers are set up to provide this in different ways, and there is always an element of risk involved in paying for these services yourself and then claiming back post-event. However, previous weather and atmospheric disruptions have generally resulted in carriers picking up the tab for ‘reasonable’ expenses.
This seems, anecdotally, to have been 3* accommodation including travel from and to the airport, breakfast, lunch and dinner taken in the hotel’s standard restaurant, and soft drinks.
If the delay is experienced at your ‘home’ airport, then the airline may take a stricter view on what constitutes their duty of care and how much they are willing to pay out. After all, you should be able to just go home and avoid additional cost. If, however, you are downroute, transferring or commencing from a port which is a significant distance from home, and/or you are in an area which is experiencing high levels of hotel occupancy, then the airline should be somewhat more charitable in terms of the level of support offered.
If at all possible, it would be preferable to have the airline arrange to cover your costs by gaining authority from the airport desk in advance, but if this is impractical then you may be left with little option but to take matters into your own hands and seek reimbursement afterwards.
Do remember though that, if you purchase non-flexible hotel accommodation and find that you can in fact depart earlier than anticipated, then the carrier does not have to pay for the unused nights.