They are heavily associated with poverty, with 30.6 per cent of homes in the most deprived fifth of areas reporting they are often or always damp, compared with 11.9 per cent of homes in the least deprived areas.
But study director Dr Susan Morton said it was surprising that dampness was so prevalent even in the richest areas.
"It's still a significant number of our children growing up in homes that are damper and colder than we think they should be for their health," she said.
The state-funded study, which has cost $5 million to set up and will cost $3 million a year, aims to follow the babies into adulthood to work out factors associated with health, wealth and successful parenting in later life.
In general, the first post-birth report released today paints a picture of much-loved, healthy babies. Almost all (97 per cent) were breastfed at least initially, 97 per cent sleep safely in a cot or basket by or on their parents' bed, and more than 90 per cent have had all their immunisations.
Ninety-six 96 per cent of mothers and 85 per cent of fathers sing or tell stories to them at least weekly and in most cases daily, and 84 per cent of mothers and 62 per cent of fathers read books to them.
But just over half of all the babies are growing up with what Dr Morton calls "one or more indicators of what you might class as hardship".
Fifty per cent of mothers said they had "been forced to buy cheaper food so [they] could pay for other things".
Eighteen per cent had "put up with feeling cold to save heating costs", 13 per cent had "made use of special food grants or food banks", 12.5 per cent had "gone without fresh fruit and vegetables often", 10.8 per cent had "continued wearing shoes with holes" and 5.3 per cent had "received help in the form of food, clothes or money from a community organisation such as the Salvation Army".
More than a fifth of families in the most deprived areas said they did not use any form of heating.
Mary-Ellen and Matthew Hinton said their daughter Sybella suffered from croup and constant coughs until her grandparents gave almost $4000 for an HRV ventilation system for their 1940s bungalow last July.
"She'd had that cough for at least a year," Mrs Hinton said. "We put in HRV and it fixed it."
But Marama and Paul Davidson, who live in a modern house in Botany, said even their joint income of more than $100,000 was not enough to pay unlimited power bills for six children.
"There are times we sit here in blankets," Ms Davidson said. "We have done things like bathing the kids in the laundry while the dryer is on because that is the warmest room."
