Coronet Peak and The Remarkables both generally operate from around June through to September or into October, but neither field runs to a fixed calendar the way a Northern Hemisphere resort with reliable snowmaking-only operations might. Both fields do run snowmaking to supplement natural snow, but actual opening day, closing day, and which runs are open on a given date all still depend heavily on how much snow has actually fallen and settled that year.
Why this matters for booking
If your trip is built specifically around skiing, booking flights and accommodation for the safely reliable middle of the season (broadly, July and August) carries much less risk than booking right at the edges — early June or late September — when a field might open later or close earlier than its typical window depending on that year's snow. Shoulder-of-season trips can still work out well, but it's worth going in with the flexibility to adjust plans if conditions are running late or early.
Where to check current status
Both fields are operated by NZSki, whose website publishes current trail and lift status, snow depth and operating hours for the season in progress — this is the source to check close to your travel dates, rather than relying on a general date range like the one on this page.