You could, but it's not how most people would phrase it. You might build on the ground in the meadow, but it's still in the meadow.
The problem is that a meadow in concept is not an area but a volume of space. It's not just the ground, but the air above it. You walk in a meadow. You throw a ball into a meadow. You picnic in a meadow. A meadow, unlike the ground within it, doesn't have a defined upper surface, so you can't do things on it.
Note: This is American English specific to the middle Atlantic region. I can't say I've heard it used anywhere else either, but I wasn't listening either.
By the way "auf der grünen Wiese" is often used when talking about construction projects outside of city limits, especially supermarkets and shopping centres.