"In the thousands of comments, people seem to be yearning and longing for their own lost childhoods, and the childhoods of their children, which are so dominated by screens," Welsh told the Guardian.
"Play is crucial for children's development, and I hope this tiny little clip inspires parents to allow them the freedom to just be kids."
Welsh told the Herald she never dreamed the video would "literally take the world by storm".
"It was lovely to hear of the joy it brought so many and also highlighted the need for us to advocate even more to ensure children get to have this experience worldwide."
Welsh said she hopes the millions of views help change attitudes and practices across the world.
"Every child deserves to be full of play, nature, friendships and unbridled joy."
Of the more than 14,000 comments on Facebook most were overwhelmingly positive, saying it was amazing to see children allowed the opportunity for unstructured, messy fun.
This is exactly what childhood is about!" wrote Dale Bowes. "Not hiding inside playing on a smartphone but interacting with each other outside, making the most of nature and outdoors. Don't bubblewrap your kids because they won't live and learn. Let them get bumps, grazes and bruises and getting soaked in the rain from having a great time! At least that's how my childhood was and it was brilliant."
Many commenters from the US said such unorthodox playtime wouldn't be allowed in their childcare centres, including a woman who worked in one.
"We would be shut down just for playing on 'wet slides'," she wrote. "Good to see kids being kids! Learning by trial and error!! Love it."
A few people raised concerns about the lack of teacher supervision in the video, or that the children were at risk of catching germs or an illness. "I see the danger of possibly lightning striking that tree, travelling to roots and hurting the children," wrote Janie Lipsmeyerfrom Texas.
"I know it's a one in millions chance that would happen, but perhaps this event should be left for the children to do in their own homes and not at a school, the business is risking a possible huge liability should it all go wrong."
Welsh said after the "spontaneous fun" was over the children headed inside to hot showers, fluffy towels and dry clothes.