Is the easement/right of way written and recorded? How is it described? This is critical because it is essential to define the exact location and scope of the allowable uses in the document creating the easement, and you should look to the wording of your specific easement for guidance. If the language is unambiguous and clearly defines the location, nature and extent of the easement, the document will stand on its own, and a court will not have to look to the intent of the original parties in resolving a subsequent dispute.
Generally, an easement does not convey the unlimited right to use the covered property. The rights of the easement owner are measured by the purpose and character of the easement. The use of the easement is limited to the use that is reasonably necessary for the intended purpose of the easement. Of course, the intended purpose is not always clear from the easement language itself. Interpreting an easement often requires an investigation of the intentions and circumstances of the parties at the time of the original grant or reservation.
Unless the easement contains an express statement to the contrary, use of an easement may be adjusted to conform to newly arising needs that the parties reasonably should have expected to develop in the natural use of the land under the easement. However, an easement owner MAY NOT materially increase the burden or impose new burdens on the underlying landowner.
In your situation, depending on the wording of the easement, a logging operation may impose too much a burden on you as the underlying landowner. I would consult with a real estate/land use attorney in your area.