The EHIC will only cover you for necessary medical treatment:
• treatment if you're taken to a private hospital in the event of an emergency
• mountain rescue costs if you're injured while skiing
• repatriation costs if you need to be flown home
• cruise holidays
And even though you're in Europe, medical costs can still hit the roof if you're not properly insured. Claims for skiing accidents can reach as high as £90,000, and an air ambulance can add further £10,000 to the bill.
So, while it makes sense to get a free EHIC card for travelling in Europe, travel insurance could give you the extra protection you need, and more comprehensive cover should the worst happen.