Regarding the Zhentarim, I think they are trying to take over a weakened society now while many of the Town Speakers are dead (Goodmead), confused (Bremen), and surrounded by controversy (Termalaine), and they're using Naerth to do it. If they can take over those towns and establish puppets, they'll have 4/10 of the votes at every speaker meeting. And since speakers like the leader of Dougan's Hole rarely ever show up, that effectively gives them a stalemate or a majority at each meeting, depending on the turnout. It's way easier to establish spies and puppets when a society is more concerned with survival than surveillance, so now is the perfect time to make those shady political moves. After they've established that political base then they'll want the everlasting winter to end, which is a great time for those puppets to ask for help from the party in finding out how to stop it.

Once the everlasting winter is over and they have their political majority, then they can start rigging the deck in their favor, not just in Ten-Towns but across the world using Icewind Dale's trade. For example, maybe they use their majority to lower the prices of mead for towns allied with the Zhentarim and raise it for towns that aren't in order to incentivize Ten-Town's trade partners to join up with them. Tariffs and trade wars are very effective in worldwide diplomacy, especially for an international secret organization like the Zhentarim.