In Jain dharma, ahimsa (non-violence) extends to all living beings, including grass and the tiny life forms living there. So walking on grass barefoot can harm unseen beings, and is generally avoided, especially in places where many small organisms might be harmed.

If you must go across grass:

• walk very carefully and slowly to minimize harm, or
• wear shoes or use a path/mat to avoid directly stepping on the grass.

There is no significant difference between Digambar and Shvetambar views on this particular point; both emphasize minimizing harm to life in all forms.