IMO, Wooden frames are NOT safe. The only time i would ever consider a wooden frame would be if like the kart is going to be used in a backyard with lots of room and its going to have a top speed of like 15-20. Anything faster than that i wouldnt use one and if it going to be used anywhere besides a backyard i would definitely not recommend one.
A powered wooden go kart had better be exceptionally well built, or restricted to very low speeds. Dying sucks. Dying with a million splinters in your @ss is the express train to he//.