"He's absolutely functional ... He's very aware. He knows exactly who we are and we've had conversations with him. He's in critical care - still extremely unwell - but he's responding to whanau."
Lieutenant Cowan joined the military from high school six years ago.
In 2007, when he was 22, he told the Herald: "I joined the army mainly because of the opportunities and the challenges this career choice presents on a daily basis."
Mrs Cowan-Greening said her brother, who is the youngest of 10 children, was very much loved within the extended family and a favourite with his many teenage nieces and nephews, whom he trained with regularly.
It was a particularly hard time for their parents, Monty and Stephanie, she said.
A steady stream of people had been coming to visit but only immediate family were allowed in at the moment.
"There's about 40-strong [here] and we're trying to hold off a lot of whanau. Some haven't even seen him - we're keeping that to a minimum, but it's very hard when a nanny comes.
"We're just hanging out, just sitting [with him] and healing each other by being together and to help ourselves get through this."
Mrs Cowan-Greening said the family had been overwhelmed by the support not only from those back home in Hawkes Bay, but also the wider New Zealand community and even well-wishers from overseas.
"There's huge support. Back home in Hastings, our people are very aware and we've been hearing that everyone's been doing big mihi to us. Our churches have been supporting us - our church members have been dedicating prayers and fasting.
"We've had worldwide support - a lot of messages and love and support have been coming to all our phones nonstop, and a lot of private messages.
"People we haven't heard from or seen in years - that's what friends and family are. You show yourself at those times. The support has been overwhelming."
Lieutenant Cowan's collapse has sparked an inquiry into selection processes for the SAS and whether they need to change.