"She said to me that she couldn't feel her arms or her legs and she couldn't move at all.
"She was begging me to take the baby out from underneath her because the baby was crushed underneath her stomach," she said.
Castell then hailed staff to assist and said it took at least five minutes for staff to respond to her and her husband's screams for help, as young children looked on.
She said her husband stopped a waiting child from tubing down the slope immediately after the accident.
Snowplanet's duty manager confirmed the incident took place but told the Herald CCTV footage showed staff were at the site within 90 seconds.
The injured woman was taken by stretcher to the first aid room and then by ambulance to North Shore Hospital. Her child was reportedly unharmed.
"We took it as the worst possible case scenario and followed all the procedures we had in place," the manager said.
While the woman was distressed, she remained responsive and alert, she said.
Snow and ice was routinely flipped off the mats at the bottom of the ramp every half hour for safety reasons, the manager said.
A spokesman for St John Ambulance said the victim suffered moderate injuries and was taken to hospital.
Castell - who had been attending a child's birthday party at Snowplanet - said she also suffered an injury yesterday, hurting her arm on the slope earlier in the afternoon.