There is a body of opinion that recommends not putting your hands in ski pole loops unless you are in fear of losing your poles, for example in deep powder snow, but this has always been a debate.
In the event of a fall, putting your hands inside ski pole loops greatly increases the risk of sustaining a Skier’s Thumb sprain. This common skiing injury is caused when the skier falls and lands on their hand or the ski pole, with the thumb in an extended position, spraining the Ulnar Collateral Ligament of the thumb. This is the ligament located in the web space in between the base of the thumb and the index finger.
This injury is also commonly seen in rugby players and goalkeepers. Immediately after injuring your UCL it is best to rest it for the first few days and apply ice for 15-20 minutes every 2-3 hours. It is wise to seek medical attention if the swelling and pain has failed to settle within the first week as this may be indicative of a more serious injury to the ligament like a partial or complete rupture, and you should rule out any associated fracture. Symptoms may include persistent pain and swelling and a sense of instability around the thumb during pinch activities. Wearing a thumb stabiliser if you have a previous history of this injury may be a good idea.