Technology in thermal underwear has come a long way...... if its a short one time trip to somewhere cold , just borrow from your friends ..... if travelling to colder climates is a constant affair just buy ONE good set
like others have said, get some thermal underwear ONE SIZE SMALLER ...... sagging long johns and tops do little to keep heat ... the new space-age type (Gore-Tex for example ) are super thin tight fitting , sweat-wicking and ultra-light AND keeps the heat so well (not cheap )
They are usually multiple thin layers of fabric to trap body heat while still allowing the skin to breathe and wick sweat away from the body ..... eg 100% polypropylene .... but not cheap ..... Isetan is selling a set for about $160 made in Japan
a beanie or hat and gloves will keep essential heat-escape points down (mittens are always better than gloves)
and a neck scarf too
Auckland and Christchurch has PLENTY of 2nd hand clothing stores where you can pick up stuff on arrival
ANYWAY its approaching Summer-time in NZ so rest easy and stop worrying