Interesting. I'm not sure I've ever tried to say something like that. I'd say you have a few options, one with masuにいく and one with ために.
スキーをし、日本猿を見に長野県に行く。 (or maybe 長野県にスキーをし、日本猿を見に行く。)
スキーと日本猿を見学するために長野県に行く。
I'm not sure how well those work or what better options would be, though.
[Edit] Never mind. There's my answer. ha
[Edit 2] Yeah, I guess my first versions say something different, like "I'm going to ski, then I'm going to go see the monkeys in Nagano." Whoops.