For state forests the stated purpose in the definition of a state forest is for resource extraction. This means state forests are designated to be logged off on a schedule. Recreation is a secondary purpose for a state forest.
It is fairly easy to get a permit to collect in a state forest. Go to local (usually county or district) state forest headquarters, and ask for a permit to collect for personal use plants for landscaping your personal home, not resale. I think standard permit allows 12 or less, but it varies by state. They will also tell you where you may collect. If you already know where you want to collect you can clear the location with them. Be patient, if you are the first in a few years, it may take a while to talk them through it. But they have the forms. Fees are not real large. Most states under $50.
This only applies to state and federal forests. Wilderness areas, State Parks, Recreation areas, Refuges, and other designated areas may have rules that prohibit all harvest of plants. Worth asking if you have a specific area in mind. But unless it is land managed for logging leases, it is not likely you will get a permit.