The conference will be early in the winter season in New Zealand. Note that Lake Tekapo is on a high country plateau surrounded by mountains and at an elevation of 762 m above sea level.
The temperatures there are typically 5 degrees Celsius less than in Christchurch.
You should expect a mean daily maximum temperature during the conference of 8 deg C (45 F), and a mean daily minimum of -1 deg C (30 F).
In June there are on average 54 mm (2.1 inches) of rain in Tekapo. There is about a 10 per cent chance of rain on any day. Snow is also possible, but the probability is quite low. There are just 9 hours of sunlight per day at this time of year.
The essential message is that you should come dressed warmly and have suitable coats and jackets for venturing outside.