In principle, a clear yes.
In most countries street painting is allowed if you paint with chalk. But there are also countries where street art in general is not allowed. These are the countries where freedom of expression and personal liberty are restricted by the political system anyway.
However, even for some countries where street painting is allowed, there are restrictions. Sometimes you have to get permission from the local authority beforehand or you have to work on a canvas or similar painting surface.
Street painting in Germany
In Germany, the regulation of the practice of street art falls under municipal law. In other words, each municipality can have its own regulation here. In Munich, for example, you have to apply for a permit and you have to work on a painting surface. In Cologne, you can get started right away on the Domplatte, directly on the ground.
What should also be a matter of course in the private sphere applies everywhere. Don’t fool around and behave properly. If you paint a nice picture, and also give a decent picture yourself, you can usually paint anywhere. If you are not sure, you can check with the municipality beforehand.
Painting with acrylic paints
Painting with acrylic paints is certainly an exception. Classic street painting is done with chalk. Some also use gouache. Both paint materials are washed away in the next rain and that’s why it rarely leads to problems with local authorities.
Many street painters, like me, now also use acrylic paints. This is partly because I want my paintings to be walkable, and partly because they are very large. We are talking about mostly 100m² and often more. My largest 3D image was 1000m².
Painted with chalk, no human could interact with the image without damaging it. Painting such a large area also takes a few days. Then when it rains, there’s hardly anything you can do. Protecting 100m² of floor with foil is a challenge that is easily underestimated.
Acrylic paint, however, is and can be very durable. In other words, you paint a picture that stays in the same place for weeks, months, or even longer. I can hardly imagine a German city center where this would be allowed without being asked.
Unless a city invites me and wants a picture that will please the citizens and guests of the city longer.
So, if you want to do 3D street painting yourself, use chalk or gouache. Should the public order office show up, you can quickly show with some water that the next rain will wash everything away.