She was surprised, but ecstatic, and said "yes".
The proposal was a new stage in a long story. The two had known each other 40 years earlier, when they were teenagers from military families. They lost touch, married others and both had grown up families.
Alone again, they started seeing each other. Their first big trip together was to walk the Camino de Santiago, an 800km pilgrim trail through the north of Spain, in September 2014. The fell in love while they were walking, Mrs Green said.
Mr Moore had to return to the US before the walk was finished. Ms Winslow did the whole 800km, and walked for a week with the Greens. It was a simple existence, with time to eat fruit from trees along the way, and to talk.
Mrs Green told their new friend about the Tongariro Alpine Crossing, the 17km walk through volcanic peaks in Tongariro National Park. She had always wanted to do it, made two attempts and was foiled by bad weather both times.
Back in the US, Mr Moore sent Ms Winslow flowers and they began a long distance relationship. They were both keen walkers, and researched the Tongariro Crossing.
When they decided to visit New Zealand and walk it, Mr Moore messaged the Greens, asking them to help with his surprise proposal.
In Rotorua, he bought new pants with a secret zip pocket for the ring because he was afraid of losing it. The Conservation Department and Visit Ruapehu chose a place for the proposal, and got a photographer there.
Mr Green made a banner for the occasion, using a greeting used on the Camino de Santiago because it was so significant for the couple. It would not fit in his day pack and he pretended he needed a tripod bag in order to carry it.
When the two couples walked the crossing the Greens made sure they arrived at Blue Lake first, to set the scene. Their banner said Buen Camino - the usual greeting between pilgrims on the trail - for Life ... Together.
The engaged couple found champagne and cheering awaiting them when they reached the end of the crossing.
Back in the US they returned to their respective homes, where they both have businesses to run. In New Zealand Mrs Green is waiting to hear what happens next, and said if there was a wedding they would go to it.
"It would be a lovely thing to round off the story."