As a general matter, it's my personal philosophy that hiking and skiing are compatible land uses.
Booth Creek (owner of Waterville, despite recently announced changes) manages property owned by the U.S. Forest Service under a Term Special Use Permit (Permit No. 4002/01) valid through 2034. The Permit authorizes Booth Creek to use and occupy certain National Forest System land for the purpose of constructing, operating and maintaining a four season resort. It's not exactly a lease; technically it's an occupancy permit.
Near as I know, no recreational users have brought serious challenges to the exclusivity of USFS occupancy permits. The challenges I know of have involved, e.g., snowboarders getting kicked out of ski resorts on USFS land for drunkenness. Undoubtedly the permittee has the right to restrict certain activities for safety's sake. Where a user is simply hiking alongside a permitted trail on USFS land, it's my understanding that the issue remains unsettled. I would guess that the legal conclusion would be that the hiker has every right to be there, particularly where the hiker isn't "interfering" with permit operations. (Note that the USFS has ruled that a permitted hut in Colorado could ban camping in its vicinity, as camping could "interfere" with the permitted operations.) Certainly a skier who bought a pass but lacked the skills to descend or ascend a steep pitch would be within her rights to click out and bareboot. To me, what you're buying when you pay for your pass is the right to use the improvements made by the permittee; typically, these include grooming -- but admittedly the improvements often include trail construction, from which a hiker would benefit.
To me, despite being involved in legal affairs, this issue shouldn't have to come down to rules, regulations, courts or enforcement. We should all have the right to enjoy our shared national heritage in any reasonable manner we see fit. To me, hiking alongside a ski trail is perfectly reasonable.
Finally, we are undoubtedly allowed to hike the Livermore Road and Trail without having to pay a fee to Waterville Valley. People will say all sorts of things, but words can't trump our freedoms.