Åka skidor is just generally ’go skiing’. ’go cross-country skiing’ is åka längdskidor. The word utför means downhill, that’s correct, and slalom is ’slalom’.
Occasionally I put a sentence into Google translate to see how close it comes to the translations here. It gets pretty close sometimes, but this time, not do much. It offered "Under vintern åker vi mycket." Where is skiing??