COVID-19 travel restrictions have been relaxed somewhat in most European countries, but increasing rates of Omicron infection and varying countermeasures imposed by the governments of the individual EU states make planning a ski holiday in winter 2022 tricky.
Here are current restrictions by country:
Austria: Be prepared to provide proof of full vaccination or recovery, plus booster shot or negative PCR test. Negative test only is not sufficient if you are unvaccinated unless able to offer proof of vaccination exemption. Rules are less stringent for teens and children under 12. Some bars and restaurants are closed, others must close at 10 PM. Masks are required on transportation and in indoor spaces. Some areas of the country (e.g., Vienna) have stricter rules than others - ask ahead.
France: Persons from France's Red List and Orange List countries are barred from nonessential travel to France. Pass Sanitaire is required to access bars, restaurants, ski lifts. To get the pass, those over age 12 must provide proof of full vaccination or recent recovery, or present a negative PCR or antigen result taken in the past 24 hours. Masks are required on cable cars and enclosed ski lifts. Restrictions are more stringent in some towns - ask ahead.
Germany: Germany classifies countries as "low-risk" and "high-risk" and requirements for entering Germany differ between the two. Once in, you will need to provide proof of vaccination or recovery in order to enter indoor restaurants, bars and leisure facilities. Negative test may also be required. Some parts of Germany (e.g., Bavaria) have more stringent requirements, and some resorts are closed - ask ahead.
Italy: Visitors to Italy must show proof of vaccination or recovery plus either a negative PCR test taken within 48 hours or an antigen test taken within 24 hours. A "super green pass" - showing full vaccination or recovery - is required for persons over 12 to access ski areas, to enter bars and restaurants, and to eat in outdoor seating areas. FFP2 or medical-grade masks are required on ski slopes and anywhere social distancing is difficult to maintain. Risk levels and restrictions vary by area within Italy - ask ahead.
Switzerland: Vaccinated persons and those recently recovered can now enter Switzerland without a pre-arrival test. A COVID certificate showing you have been vaccinated, recovered or tested negative is required to enter bars, restaurants and other indoor facilities. Masks are required in cable cars and on lifts. Some resorts have stricter requirements - ask ahead.
By the way: There's plenty of skiing in the USA. And most vaccinated foreign citizens can enter the USA on an ESTA visa waiver. (Most air passengers headed to USA - vaccinated or not - will have to show negative results of a test taken with 24 hours of boarding, and provide contact information to the airline.)