Take Heart!
From Christian Vegetarian Association (CVA)

The Many Problems with Grass-Fed Beef

People think that grass-fed beef is better for the environment and more humane; however, grass-fed cattle contribute more to global warming than grain-fed cattle. Moreover, grass-fed cattle still suffer mutilations without pain-killers and still meet the same horrific death at industrial slaughterhouses. And, if these reasons were not enough, the fact that biodiversity (both, fauna and flora) is lost when cattle are allowed to graze should make people think twice about buying grass-fed beef.

Please visit Pseudo-Sustainability: The Beef With Grass-Fed Beef.

It's true that farmed animals who are raised outdoors, such as in the case of grass-fed cattle, tend to have a less abused life because they are able to exercise some of their instincts and fulfill some of their needs. However, they are still exploited for their meat, eggs or milk and killed at a young age, most likely involving terror and pain.