In FotR, a fox comes across the three hobbits (Sam, Pippin and Frodo) and ponders over them a while, thus indicating sentience. It's not specified anywhere that I've read, but I've always assumed most, if not all, animals in LotR are sentient/can reason. In Bree, Strider and the other rangers are rumoured to be able to speak with birds and animals and in a few places other characters comment on how some of the birds might be spies or working for Sauron (I think).
I might be a little biased on the topic of animal sentience, though, as I'm an animal communicator.
