Winter sports lovers are still taking big risks on the ski slopes and one in three are under-insured.

A survey of 3,500 insurance customers found 34% would not wear a helmet whilst ski-ing or snowboarding. It follows a survey by Columbus Direct in 2013 which found 38% saying they did not wear helmets on the slopes.

Despite high-profile accidents to actress Natasha Richardson and Formula 1 driver Michael Schumacher, when asked directly whether those incidents might make them think again, 60% of the free spirits said it would make no difference.

The survey found 50% of enthusiasts admitting to not carrying any safety gear at all whilst on the slopes. This was most prevalent among the 50-plus age group, with over two thirds saying that they would not consider a helmet compared to 39% of under-50s..

Greg Lawson, managing director of Columbus Direct said: "Like most travel insurance policies, wearing a helmet is not compulsory under our policy. However we do strongly recommend protective gear such as a helmet and wrist guards to help defend against fractures. Compacted snow on the piste can feel like concrete when you land on it at speed so it's well worth the investment."

Three-quarters of over-50 skiers, and 70% of the under-50s, said they were happy to disappear off-piste on their own.

Lawson said: "When venturing off-piste we recommend you always go with a guide or an instructor. Off-piste slopes have not been prepared by snow ploughs, so rocks, cliffs and sudden drops may not be easily visible. The greatest risk , however, is avalanches."

Sainsbury's Travel Insurance research found that among winter policy buyers, only 29% are interested in off-piste cover. It also found damaged knees are the most common injury sustained on the snow, with 9% of those planning to go away this winter having previously suffered from a knee strain. Some 7% have endured a broken leg or a facial injury respectively, and 6% report ankle sprains or a dislocated shoulder.

One in three people planning winter recreation will not be properly insured, according to travel agents' group ABTA and the Foreign & Commonwealth office.

Experts say do not rely on the European Health Insurance Card as it will not cover the full costs after an accident, such as ambulances and repatriation. Choose a policy with £2 million of medical expenses, which sounds high but is standard, and £1m of personal liability - in case you crash into anyone or their property.

You should also have cancellation and curtailment cover. Gocompare.com has found that 100 travel insurance policies on the market, around one in five, offer no compensation for piste closures.

Piste rescue should also be on the policy - it may seem unlikely but a helicopter airlift can be expensive.

Insurers will not pay out if you are negligent, leaving your skis in a bar for instance, and Columbus Direct warns: "Watch your drinking: most policies have exclusion clauses if you are under the influence of alcohol."

If the worst happens, don't rely on your passport. The FCO says: "We provide support for British nationals who get into difficulties overseas. However, we cannot pay medical bills if you are hospitalised and we can't arrange to fly you home."