As of 1 January 2022, everyone skiing in Italy must hold liability insurance which covers damages to third parties. You also need to have a document with you, which proves that you are holder of such an insurance!
Many people already do have such an insurance with the default and often obligatory household insurance. What you need to do: clarify if skiing accidents are included in your insurance, and request the document which proves you are holder of such an insurance!
If you are not holder of such an insurance, you could buy one here: https://www.dolomitisuperski.com/en/Vacanza-invernale/Assicurazione
Please note: in South Tyrol and Italy there is - for safety reasons - a legal alcohol limit also for skiing and snowboarding! Like while driving a car the limit is 0.5 per thousand. Over 0.8 per thousand the sanctions could really be hard!
So please do not drink and drive, ski or snowboard!