There is quite a range of private companies in forestry. Some like Plum Creek, Weyerhaeser, and Potlatch directly own large tracts of timberland and manage them for production.
Weyerhaeser is pretty vertically integrated and even has its own research division.
What you also see a lot of these days are investment funds.
Companies like Lyme Timber own lots of land and pay share holders profits from the management. Consulting firms can be either pretty big operations like Prentiss and Carlisle, just one forester or anything in between. Consultants don't own their own land, but private landowners pay them to do management. This can be on the scale of Lyme Timber paying Prentiss and Carlisle to manage 200,000 acres, or one forester working on many different privately owned 200 acre mom & pop family woodlots.
People with a 4 year degree can easily get into field work. It's easier for someone with a 4 year degree to get into academic stuff than it is for someone with a 2 year degree.
And as for work in the government, in my opinion it's very difficult to get permanent jobs with the fed. I have several friends that did seasonal work year after year with the USFS for and yet they did not get permanent placement when the graduated. Yet, if you do land a full time job somewhere you can probably expect to keep it until you die if you want. With the USFS, you have the opportunity to move up and move around. But the problem is, there are a lot fewer opportunities when you want to stay in one place vs opportunities for 150 National Forests across the country.
The more opportunities you can take advantage of, the more that will be provided to you.