It's a fairly poetic meaning, so it isn't a strict language issue. He needed to rhyme with the last line. The general term for this is "poetic license" which means we often permit poets to bend the rules quite a lot in order to get something that sounds good.
But basically, he is referring to the observation that when trees get very cold, they can produce loud cracking noises. This is because water expands when it freezes, so parts of a tree can swell when they freeze. This often causes the fibers of a tree to split apart. Since it is the living part of the tree that will have water in it, that's the part that can split. It is the "heart" of the tree in a manner of speaking.
To rend a thing is to tear or rip it. So to "rendeth" is an archaic way of expressing to rip something. And "by the board" means to do it board-by-board. That is, the parts of the tree (the boards of the tree) are split apart.
The picture shows an example where a tree split open from freezing, the sap flowed out, and then it froze.