I did get an email reply from GPNF:
"Geocaching is a permissible activity on the Gifford Pinchot National Forest.
Geocaching is prohibited in Wilderness, Natural Areas, Research Areas, and
the restricted zones of the Mount St. Helens National Volcanic Monument.
The cache needs to be located so that user trails are not created. For example
along a trail or adjoining an existing site.
Here is a link to a map showing the restricted zones of the Monument.
I take that means no permission needed - just need to follow their rules, along with the geocaching.com rules, of course.