Make Player Move Slow Over Grass

Hello.
I have this overlay:
alt text

And I want to put it over my simple 2D map, and I want it to behave so that, when the player walks over it, he is slowed down. Does anybody know how to achieve this, perchance?

One slightly complicated way could be to create some 3D surfaces in a modelling program to mimic the shape of the grass patches, and use them as mesh colliders. You could cast cays downwards to see if you hit them. This would work, though it would be a bit complicated having to model all of those patches.