Consider perhaps that they did not exactly "choose" to do so. I think it was more like what could be compared to a heaviness that one might experience with certain kinds of drugs.
Let me recount a personal experience I had that I think makes an even more fitting comparison. I was always a vivid dreamer but like so many people, I had difficulty remembering a lot of the details of my dreams, so during one period of time I decided to keep a dream journal. It proved to be very effective as a means of recalling the dreams but there was a totally unanticipated side effect. I would have days that being awake seemed more like dragging a painfully dense physical body through a dream. And it was literally almost painful and completely beyond my capability to control. Try to imagine moving through an atmosphere with the resistance against you something like that of moving underwater and you will get the idea. It seemed to be not such a great idea to muddy the boundaries between waking and sleeping.
I suspect that it was something of that kind of irresistable heaviness that the hobbits were experiencing. Add to that an other worldly sleepiness combined with their already tired bodies, and it makes sense that they couldn't help but succumb.
Now, that said, there is a question I have. Perhaps it is answered in the book but I have been good and not read ahead and I don't recall from earlier readings. What was Tom Bombadil's relationship with the trees? He reminded me of a kind of Middle Earth Paul Bunyan in his general presence and demeanor. Did he just "happen" along at that time or did he hear their call for help? Or did he perhaps learn of their presence from the trees themselves?
Spoiler Alert?
Is this the guy that turned into a bear or something like that?