The trees in the "thickly wooded swamp" are hemlock trees as reported toward the end of the story. According to information given earlier in the story it is possible the tree that was hit by a thunderbolt had Tom Walker's name engraved on it, just like the other trees in the grove which were pointed out to Tom by the "black woodsman" or "old scratch" when they meet. Other wealthy men, Deacon Peabody and Crowninshield, had their names on trees which were eventually brought down. The "black woodsman" notes that he uses the downed trees for firewood. When Tom is taken at the end of the story by a black man on a black horse, they are last seen going "like mad" into "the black hemlock swamp towards the Indian fort," which is the setting where Tom makes his deal with the devil. It is appropriate that it was a hemlock tree since the tree is considered quite toxic and hemlock a well known poison (most famous because of its link to the death of Socrates).
I do not think it matters what tree was hit. Either way, the effect was the same. Everything burned down. This is definitely a reflection of Tom Walker and the type of life he lived, and what happens when you make a deal with the Devil.