Well do they? the fact that I can burn wood would seem to indicate to me that trees are at a lower entropy state - they have stored energy that can be released by oxidisation (burning).
Why do I care? I am intrigued by the notion if plants evolved before animals (which they did) then animals could be an entropic inevitability. The universe is working towards a higher entropy state, the out-pouring of energy from the sun being perhaps the most visible local example of this. If plants collect and store usable energy then they are lowering the universe's entropy a little - some of the sun's energy is locked-up and therfore not available to heat the rest of the universe.
Therefore the universe needed a way of unlocking this energy, and the faster the better, therefore animals evolved to break down the plants. If this is the case then there are some far reaching consequences.
It affects our place in the scheme of things, we may be top of the food chain, but that makes us bottom of the entropy chain. Plants are not here to provide for us, we are here to digest plants.
It also suggests that our current voraceous appetite for burning carbon is somehow our destiny. Entropy will not be satisfied until we destroy all plant life on the planet...