Many people try to cut the cost of a winter sun or snow break by going without travel insurance.

But for those unlucky enough to need overseas medical treatment, the financial pain can long outlast the physical discomfort.

Saga Travel Insurance says one in 10 over-50s and one in five younger people have gone abroad without insurance in the past five years. In the 25 to 34 age group, almost one in three have travelled without cover.

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Some wrongly assume that if their destination is in Europe, it is enough to have a European Health Insurance Card (EHIC), while others simply think nothing bad enough to warrant insurance will ever happen to them.

But without insurance, problems such as cancelled flights or vanishing luggage can leave a traveller badly out of pocket. Health emergencies can be particularly disastrous, and in some countries will result in a bill as big as a mortgage.

According to Saga, getting treatment after breaking a leg in France can cost the equivalent £10,000, while US hospitals charge as much as £45,000 to treat the same injury and £80,000 for a heart attack.

Roger Ramsden, the insurer's chief executive, said: "Not packing travel insurance can be a costly mistake. Paying thousands for a cancelled holiday or medical bills is sure to wipe the smile from the most genial of globetrotters' faces, so it's important to make sure everything is covered from the moment you book."

Anyone visiting Iceland, Norway, Switzerland, Liechtenstein or an EU member country should have an EHIC, which entitles them to receive the same medical treatment as a resident.

The cards, which are free, last for five years – but every member of a group, including children, needs their own. You can apply on behalf of the whole family online ( or phone 0845 606 2030.

But not all countries have a free health service, so there could still be a charge for basic care. And the EHIC doesn't cover private treatment, or costs such as mountain rescue in ski resorts, air ambulances, being flown back to the UK, or replacing lost or stolen property.

This means it should never be seen as a substitute for a comprehensive travel policy (with winter sports cover if appropriate), which will pay out in all these eventualities.

According to Sainsbury's Bank Travel Insurance, the average claim for snow sports injuries last winter was £3483 in the US and Canada, £1972 in Austria and £1600 in Switzerland.

Insurance manager David Barrett said: "Travel insurance, with the appropriate winter sports cover, is essential for any trip – especially when you consider that it will also pick up the bill if you need to be transported to hospital, including airlifting you off the slope, a cost that can be very high for some destinations."