panthro, its funny you asked that because i was just reading some old posts elsewhere that discuss this very issue. i also like to think i have a leg up on this issue because i have worked for both the state and federal government agencies that manage oregon's forests, which is really neither here nor there in regards to your question. . .
the answer is that the majority of public land does not have rules specific to tree climbing, meaning that you could walk up to any tree and climb it. however, I read that in sequoia kings canyon national parks you are not allowed to climb the giant sequoias. Here in oregon, there are no parks like that, so really any tree in any public forest is open for climbing, besides tree's of special interest like the Klootchy Spruce or Octopus tree.
but there is really more to it than that. here in the Specific Northwest, there are many tree protests, which involve tree climbing and tree sits. this is illegal for several reasons, which makes it big news here. The result is that the general public thinks that any tree climbing outside of professional work is unlawful. So, when Joe Blow sees you climbing either in the neighborhood park or deep in the national forest, they may misunderstand your intentions and be inclined to tip the authorities. Forest police officers dont need rules to make you leave, and they would just assume not see you there climbing trees. So, really, its not illegal but looked down on in a way that makes a person want to climb trees clandestinely.
Finally, I think climbing biggest and most notable trees is looked down on by most everyone. I would love to climb that cottonwood in my original post, but at the same time, i dont think its a good idea.
Im sure this is more than you wanted to know. and panthro, if you read this far i sent you a pm elsewhere if you catch me