If Bosmer are not allowed to cut down trees because of theyre pact, how can they have bows, because bows are mostly made of wood.

Bonemold and Chitin yo. The Dunmer don't have those markets all to themselves, and the Bosmer pretty much follow the "Waste not want not" to a T.

That, and there's nothing stopping outsiders from using these materials and selling them, if they have to be made out of wood, which is unlikely.

Bows were historically often made of horn.

Maybe they crafted the bow from a broken branch after a storm or from the wood from a broken cart.

Yes, but I don't recall any horn bows in Oblivion or Skyrim. It's a shame they havent made one based in the Bosmer homeland, we would get a greater idea on how their society works.

There were Chitin bows in Morrowind. Chitin is horn-like-ish (It's made from insect shells that have been glued together)

Because those don't take place in Valenwood. The Green Pact is considered to only extend to flora in Valenwood. The Bosmer are more than happy to use wood harvested outside of Valenwood.