Alpine Ski
Released: 1982
Pitch: Challenging downhill skiing including racing, slalom, and a jump competition.
Alpine Ski is...a skiing game! And pretty difficult too. The first event is a race to the bottom and man alive, is the course ever littered with things to crash into! You have two minutes and lose ten seconds everytime you crash. The action button accelerates your skiier but you'll wipeout fast if you hold it down. The second event is the slalom, which I got to only once and I don't know why I lost. The third event is a jump competition and I'm taking it on faith that it exists. It's probably really hard.
P.S. I finished Taito Legends and I'm onto Taito Legends 2 now! I like the menu layout for the games much better than in the first collection and there are a lot of '90s era arcade games in this collection (Alpine Ski notwithstanding), whereas the first one seemed heavy on the '80s. We'll be jumping a decade ahead for tomorrow's game.
I think the last skiing game I played was on Atari, Activision's Skiing. No wait, I played Steep recently but mostly on a snowboard.
Is Space Dungeon in any of these collections?
Doesn't look like it 
What's that game like?
For some reason, I remember seeing Alpine Ski in nearly every arcade I went to as a kid for a while. Some Taito games like this and Jungle Hunt seemed very prolific in the arcades around me back then.