What was used as grazing land in the New England villages?

The answer to this question depends on when. Over the course of New England history, the grazing lands changed. The earliest settlers had few good grazing lands. There was a great shortage of grass in New England (as it was mostly covered with forest) and the native American grasses were not very nutritious for livestock compared to European grasses. Early settlers grazed their stock in the forest (which made for poor forage) or on salt marshes near the coast. Almost all other cleared land was too valuable for crops to let animals graze it.

Early on, by the end of the 17th century, English grasses and clover were being sown in New England to improve the grasses for grazing. These were mostly sown on cleared land (de-forested), and especially on uplands and hillsides. (Cleared flatlands and valleys were too valuable for crops to be used for grazing.)

By the late 19th century, crop production in New England had declined greatly, due to depletion of the thin New England Soils, and access to cheaper Midwest grains via the Erie canal. Cattle and dairy became the main New England farm products, and now cattle were grazed on some of the valleys as well as the uplands. Most of the valleys and flatlands were planted in grass, but most the best lands were still not grazed, but rather harvested for hay, to feed the cattle in the winter, and as a cash crop to sell to towns to fuel the increasing number of horses used for transport.

By the 20th century, farming in New England was in steep decline. Marginal farms and farmland was abandoned and the forest were spreading across New England again. Upland pasture tended to be abandoned, and horses and the few remaining dairy cattle grazed the valleys and flatland fields.