"graze on" or "graze in"?

Let's see the top40 grazing on 35 000 first.

Instead they graze on shop-bought snacks throughout the day.

Her son was grazed on the hand and back by bullets meant for Simpson.

Dusty paths meander among the homes and cattle graze on the grassy distances between houses.

They presented a restful and pleasing picture as they grazed on the hill near the big mimosa tree.

Periodic samples taken made it possible to assess the influence of the intensity of grazing on their productivity.

People began to ask him permission for bringing their riding animals which were grazing on the hillocks near Medina.

A child who doesn't have a full breakfast and dinner will always feel the need to graze on whatever catches their fancy during the day.

Not one, but a family of three moose came out of the woods and started diving into the lake, probably to graze on the underwater vegetation.

If supplementary feeds sourced from selenium-deficient areas are fed to animals grazing on land with marginal selenium levels, a deficiency in the horse is likely to occur.

In that day your cattle will graze in broad meadows.

This is shown by simulation of grazing in the form of mowing.

A herd of cows is grazing in his field (where the main noun is? herd?).

Sheep are always grazing in suicidal places - I think they're too stupid to realise the danger.

We stand in a field of sacred cows grazing in a field where the flowers of unreason grow profusely.

We had just passed impala grazing in the bush and gangs of turkey scavenging for food beside the road.

As I entered the compound of the house, I peeped out through the ajar gate and saw a herd of camels grazing in the desert.

As I reached his house, I noticed some horses grazing in a field enclosed by wooden fence, not too far away from the main house.

Uncovered horses grazed in paddocks should receive infrequent washing only, to avoid removing grease from the coat which is essential for warmth.

Would the following grammatical rules help to further clarify the phrase in question? ? A herd of cows that belong to the farmer are grazing in his field? (where? is/are grazing? is the contention).

Grassland, swollen with the mounds of extinct volcanoes, is grazed by cattle and roaming posses of wild horses.

He attributed the change to the increase in grazing for sheep and cows, the need for firewood, and the building boom.

Generally, however, horses and ponies intensively grazed with others require regular 6-weekly worm control.

In other words, farmers put their chickens on some kind of low grass/weed mixture that's probably been kept tree-less through annual bush-hogging and/or grazing with other animals.

Yet, like the Thoroughbred horses that graze near his Lexington, Kentucky hometown, he can sprint.

Villagers bring their cows to graze outside the classrooms.

Modifying riverbanks and livestock grazing up to the edge of streams wrecks the habitat, and leaves the vulnerable wee whitebait eggs out to dry.