When and how is person chayav on shabbos for ploughing. For example is a woman with a buggy allowed to push it on the grass, or can she not. The problem for ploughing is that you need to have a intent for improving the ground, So what are the issues for certain things when clearly one who does things on grass isn't doing the actual malacha which needs to be done?
Rabbi David Ribiat in The 39 Melachos, Volume 2, in Choraish says as follows:
"Pushing a carriage or stroller on bare soil (even soft earth) is similarly permissible even if a distinct wheel-mark appears. This is because the rolling motion of the wheels does not loosen the soil, but rather compresses it (similar to a steam roller that compresses the earth beneath it, only a much smaller scale). Compacting the soil does not improve it in any way for planting and is therefore not Choraish. (However, one should take care to lift the wheels of the carriage when turning on the soil so as to avoid scraping up dirt with the sideways movements)."
See also Minchas Yitzchak Volume 2:114:12 where he brings in the name of the Minchas Shabbos that permits this.
A buggy is allowed to be pushed on grass on shabbos even it if causes furrows (Shmiras Shabbos 28:48). Take a look at Shmiras Shabbos 26:19 and the footnotes there to get some idea on what is allowed with respect to walking on moist/dry grass on shabbos. It's not comprehensive but it brings a couple everyday examples that seem to be what you are asking for.