Hypothetically, would literal tree-hugging (i.e. chaining myself to a tree) be an effective method of protest and prevention? Would the loggers cut me down anyways? Just a random thought.
Depends on what you mean by "effective." It might delay them for a few hours or a day. There's a long history of this kind of thing, although it's usually more effective to do a treesit rather than a lockdown for trees. You could do a lockdown on equipment like bulldozers/feller bunchers though. The Earth First! Direct Action Manual has a lot of info.
Be prepared to be literally tortured in various ways, including pepperspray placed directly in your eyes, pain compliance holds, or they just cut the chains/lockbox you're in and if you get cut with it too bad.
Personally I'm not a big fan of get-arrested-on-purpose types of direct action, but it has its uses. I strongly recommend that if you're going to do something like this you connect with a group that knows how to do it and you have a support crew, including jail/legal support.
Sure, lab safety goggles will protect you from pepper spray in most instances. But what eye protection you're wearing won't matter. You're chained to a tree. The cops can do literally anything they want to you, including ripping your safety glasses off and emptying a can of pepper spray directly in your eyes. See: the infamous case of the Pepper Spray 8
Deputies pepper sprayed Mike McCurdy (above) and Noel Tendick directly in the eyes at close range while they were locked together through the tracks of a Pacific Lumber bulldozer on an old-growth redwood logging site. The activists endured the torture and did not unlock. Deputies then safely cut them loose with a portable grinder, as they could have done without using pepper spray, and as they had done hundreds of times in previous years.
That relies on the loggers fearing a murder charge. In Trump's America, would a logger be charged with murder for "accidentally" killing a tree hugging protestor?