There is a Singapore Club in Christchurch (South Island) and last I heard, there were about 100+ Singaporean families living in Christchurch. The numbers are gradually increasing year by year.
As for the cold, getting a well insulated home and good winter wear would definitely take care of the cold season. But one would eventually acclimatise to the 'cold' and shorter sunlight hours of Winter.
Your DIY needs are surely taken care of with the many large stores like Mitre 10, Bunnings, Placemakers etc. Asian Grocery Warehouse Stores are mushrooming all over Christchurch as well as many Asian take aways/dine ins too.
Cricket, Rugby and Netball are the National Pastime sports of NZ.