The practice of managing or caring for woodlands is known as forestry. If you like the sound of all of those trees, some jobs associated with forestry include conservationist, park ranger, and timber manager.
The word forestry, defined in the 17th century as "privilege of a royal forest," comes from the Medieval Latin forestem silvam, "the outside woods." By the mid-1800s, the word began to be used for "science of managing forests," a meaning it still holds today. The term actually covers a lot of (heavily forested) ground, including preserving endangered trees, protecting the habitats of animals that depend on forests, and keeping humans safe from forest fires.