Question

1. They are skating in an ice rink.
2. They are skating at an ice rink.
3. They are skating on an ice rink.
(Which one is correct?)

4. We are going to ski at a ski resort.
5. we are going to ski at Yongpyeong Ski Resort.
6. We are going to ski on a mountain.
7. We are going to ski in a mountain.
8. We are going to ski at a mountain.
(Which ones are correct?)

Answer 1

In the first set, all three are correct, but I'd choose 2 -- or say "on the ice".

In the second set, 4 and 6 are correct, and 5 will be correct when there's a capital at the beginning of the sentence!!

Answer 2

I am actually an ice skater!
the first three sentences are all correct.
4 and 6 are correct.