Skiing
Santiago is not too far around 1.30-2 hours from downtown depending on the centre from some great skiing. Not too expensive and they hire out all the equipment you need at the resorts. Some of the tour companies offer the service.
In order to work in Chile, a working permit needs to be obtained, which can be accomplished with the sponsorship of an employer. However, numerous people work illegaly, but it is obviously best to obtain a permit.
Mountain climbs
Many mountains are found in and all around Chile that are great for climbing.