I was in NZ over easter a decade ago and recall all the stores including petrol stations were closed (I had anticipated restaurants being closed and had packed a picnic lunch, but didnt expect gas stations to be closed too). Te Anau is a very small town, maybe 1000 people, so anything not tourist-specific is likely to be closed for 3 days at easter. Even tourist-specific things, like hotel restaurants, are often closed. Best to check ahead of time for the specific place and activity, these are the most likely days to be closed all year.