The fact that other aircraft were landing is completely irrelevant. All that tells you is that the weather was above the minima, and it tells you nothing about how it relates to the alternate criteria. In very simple terms, the minima might be a cloud base of 500', but the requirement for an alternate might kick in at 1,000'.
If I recall correctly NZ has a rule that any aircraft arriving from outside of NZ must have an alternate if the destination only has one runway. So, if that's still the case, you'll need to have a look at the weather at the possible alternates.
And we don't ask other aircraft for the weather. That's what ACARS is for.