Wait, why should it be strange for Winn to negotiate with Weyoun? As Kai she was the spiritual leader of Bajor and there was apparently at least some connection between the Vedek Assembly and the Bajoran government. It could be that as Kai she would have an important role in negotiating with foreign governments (remember Bareil was on a diplomatic mission to the Cardassians when he died).
As a religious leader, it might make sense that she would provide an opening for negotiations to take place, perhaps that she might be involved on some level. Ultimately, it's the leaders of governments who hammer out the details of treaties, something that Winn admitted was outside her purview.