She said Quinntana was asthmatic and his condition had worsened since living there. He had also picked up other illnesses, including scabies.
"Ever since we've been in here he's been sick.
"If you were stuck in this sort of situation you wouldn't be able to call this home," she said.
The situation has one advantage: the rent is cheap.
The couple pay $180 per week, and do not have a tenancy agreement. They never paid a bond.
The house is owned by Crossford Properties Limited, of which Masterton Mayor Garry Daniell is one of two directors.
Two days after Ms Cooper spoke to the Times-Age, Mr Daniell came to the house with two rolls of insulation.
"He just said 'here's some Pink Batts' but my partner has to get up and do it himself.
"At the end of the day it's just to keep my son warm, I'll do anything for him."
The Building Act requires new homes to be insulated if they are built post-1978.
Ministry of Business, Innovation and Employment media advisor Britton Broun said if a house is built before that time there are no insulation requirements on the landlord.
Mr Daniell said the house was about 80 years old, so it is outside legal requirements of insulation, and felt he had met any obligations he might have.
"People have lived in there for 80 years without any difficulty at all and suddenly somebody wants insulation.
"There must be dozen of houses like this in Masterton and why should I be picked on?"
Mr Daniell said the couple asked for insulation about three months ago but he wanted evidence their son was asthmatic.
"I asked them to provide a letter from the hospital, they are worried about their child ... I've never had that letter."
The Coopers say they are now looking for a new house to rent, but have been turned down by one agency. They say they will keep trying.
Cold comfort
The Energy Efficiency and Conservation Authority (EECA) have insulation subsidies for landlords with tenants who hold community services cards.
Real estate agencies are within their rights not to take a tenant on, providing they are not discriminating against them.