Goats were surrounding us. A few hundred of them. All white, with foot-long ridged horns, they were elegant but slightly menacing — at least to me, a born and bred New Yorker who has always been a little bit wary of farm animals.

But my daughter, Sonia, and her best friend, Matteo, both 3 at the time, were standing on the side of the stables, arms extended through the metal bars, holding out palms full of brown food pellets to the creatures. One goat started eating straight from my daughter’s little hand, its long pink tongue sandpaper rough, and she was giggling.

We were at the Geitenboerderij Ridammerhoeve, a biodynamic goat farm in the Amsterdamse Bos, a forest on the southern edge of the city. We had biked there in about 30 minutes from our apartment in the center of Amsterdam, with two children shoulder to shoulder in the box of my bakfiets, a Dutch bike with a kind of wheelbarrow on the front.

Amsterdam is something of an urban jungle, with apartments stacked tightly in three- and four-story buildings, and streets are congested with cars, trams, buses and ever-present bicycles — about 800,000 of them. But thanks to Dutch tradition and some clever planning, almost every city neighborhood has either a petting zoo or a children’s farm.

As a working single mother without a car, I’ve relied heavily on Amsterdam’s local farms for exposure to nature and much-needed fresh air. When Sonia was born, we went a few times a week to Zimmerhoeve, a farm built on the site of a former iron foundry. It sits on the bank of a wide canal where steel barges and cargo boats glide through dark-green waters under a black drawbridge, adjacent to a sandbox and a wooden playground resembling a pirate ship. Through the open red barn doors, we find sheep, chicken, goats, a pair of grunting pigs and a pen of longhaired rabbits we could join in the hay for a cuddle.

We celebrated Sonia’s first birthday there. Then I invested in a solidly made city bike with a baby seat, popped her on the front and off we’d go to the nearby Westerpark, which has a larger children’s farm in the center of a sprawling park built on the land of a former energy factory. Westerpark features rare red and white Lakenvelder cows, two Shetland ponies and a giant Yorkshire pig named Motti. After pushing Sonia on the swings for a while, I’d sit and drink a cappuccino while she pedaled around on a green and yellow plastic tractor.

These reused industrial spaces transformed into throwback barnyards with old farm animals, right in the urban center, seem somehow uniquely Dutch to me, although I know that there are petting zoos in other global cities. I assumed for a long time that these children’s farms had been either here forever or that they were part of the 1970s back-to-the-land movement. In fact many of these farms were established more recently, in the ’80s and ’90s, with great payoff for the urbanites of the 21st century.

Corine Riteco founded Geitenboerderij (Goat Farm) Ridammerhoeve with her husband, Willem Dam, in 1988. Wanting to demonstrate the benefits of organic farming to an urban population, they drafted an extensive proposal to the Amsterdam city government, asking to rent land within the forest, and the request was granted.

“We liked the goats because they’re such pleasant animals, and they like the attention of people who come in, and of course the baby goats are very cute,” she said. “We make cheese and buttermilk and yogurt,” she said, “to make it attractive for people to come and do their shopping here. We do sell the meat as well, and we started with the goats, but we now have chickens and we sell the eggs, and people can pick their own eggs.”

The Ridammerhoeve farm is a working farm that sells its products, but most of the others fall under the heading of kinderboerderij, as they’re called in Dutch, or children’s farms, which are petting zoos where visitors can touch goats, sheep, cows, rabbits and guinea pigs and, if they’re more adventurous, pigs and chickens. Thanks to these local farms, my daughter, who has grown up entirely in the city, feels perfectly comfortable around farm animals.

Michele Hutchison, an author of “The Happiest Kids in the World,” a new book exploring why Unicef in 2013 rated Dutch children highest in the world on measures of happiness, said that many of the ways those children are being raised today may look old-fashioned, but that this is more of a conscious choice by contemporary Dutch parents to resurrect old-fashioned family values: fresh air, nature, unsupervised play.

“Dutch kids’ parents played outside unsupervised when they were young, and now they consciously try to allow their children to do the same,” she writes.

When Sonia was big enough to sit upright, my father surprised us with a classic Dutch bakfiets, which makes traveling 30 minutes to the forest, with more than one child, a picnic blanket and basket on board, perfectly doable. And that’s where we found ourselves surrounded by all those goats.

Entering the Geitenboerderij Ridammerhoeve, we stopped first at a huge labyrinth made of tall hedges, where Sonia and Matteo disappeared for about a half-hour. Matteo’s parents and I tracked them by their laughter. After stopping to say hello to an enormous spotted pig rolling in a mud puddle, and waiting while our children climbed through a wooden jungle gym and escaped via the slide, we entered the cavernous goat barn filled with yellow hay, hundreds of goats and a startling, pungent odor. All around us, children were feeding the animals, some with the pellets bought for a coin from a dispenser on the wall, and others were feeding the baby goats with miniature baby bottles full of goat milk.

On the way out of the barn, we stopped for a moment in the shop, where we bought some of that fresh buttermilk and goat cheese, but not the meat — I’m not a vegetarian, but after feeding the little goats, it seemed a bit cruel.

Ms. Riteco, one of the founders, expressed a sentiment that’s shared by many parents in the Netherlands: “It’s very healthy to bring your children into contact with animals in farms; then you have stronger and healthier kids.” She offered a tip: Baby goats are born in January and February, and again in March and April; other newborns come in summer. Last August, 10 piglets were born.

“Children have a natural bond with animals anyway, so it’s good that they’re being given a possibility to explore that,” Ms. Hutchison said. “Play here isn’t sanitized; it’s not fenced off.”

An association for Dutch children’s farms has about 300 member farms throughout the Netherlands. They say they receive nearly 30 million visits a year. Amsterdam has about a dozen official ones, usually run by a couple of part-time employees and lots of local volunteers, and there are also other playgrounds where animals are part of the scenery.

When my daughter was about 2, for example, we favored a tiny playground off a side street in the Jordaan neighborhood that we nicknamed “the chicken park” (its real name is Vereniging Kippen en Konijnenren Slootstraat). It has a pen full of chickens and rabbits set between the seesaw and the climbing frame, and plenty of little bikes, scooters and other toys appropriate for toddlers, which are always left there for public use (remarkably, no one steals them).

I’ve been to at least two farms in Amsterdam — Erasmus Park on the western side of the city and De Werf on the eastern side — that have adult male peacocks wandering about, impressively regal when they flourish their feathers, but quite intimidating when they hiss defensively.

In De Pijp, a neighborhood to the southeast of the city center, filled with sidewalk cafes, young designers’ shops and fusion restaurants, the Kinderboerderij De Pijp, founded in the late ’80s, has two donkeys and two ponies, which small children can sometimes ride, as well as three pigs, goats and sheep, ducks, geese, rabbits and three cats. Activities include crafts workshops and opportunities once a year to watch the sheep being sheared (this year on May 14).

These days, I have a partner with his own two children, who has a car, and together we journey outside the city more often to enjoy nature. Since Sonia is school-age now, with lots of birthday parties at children’s “fun palaces” with names like TunFun and Candy Castle, we go less often to our local kinderboerderij. But occasionally I’m nostalgic for those early days, and the memories of strapping Sonia into the baby-carrier and walking down to the local farm to watch the boats glide by on the dark green canal, and to sit quietly and pet the longhaired rabbits.