I also have wet and cold mod 3rd from the top with a bunch of visual and npc mods in use.
Well, first off, if you have any weather mods, put W&C under it. As for your problem accessing the menu, I had the exact same problem. I fixed it by uninstalling it when I decided to start a new character - then after I'd made the character re-installed it and it worked fine.
Since I'm guessing you won't want to start a new character on account of a single mod, I'd suggest uninstalling it, loading in your game and acknowledging it's no longer there, then make a new save. Force quit (if you're on XB1 press the Xbox button, highlight Skyrim on the dash, Press the button to bring up game options, then quit). Start the game, load the save to make sure it's ok, exit normally to the game menu. Re-install W&C, exit to game menu. Quit to dash, restart, load back in, load the game. See if you can access the menu for W&C - if not save and force quit again, then load back in and try again.
If that doesn't work, I must have been able to get it working again because I made a new character.
Yeah, it will work with AS, I use that Mod myself. I have no idea then tbh, all I know is it was working fine until I updated it, after that I couldn't access the menu until I started the new game, my guess is the update conflicts somehow with the save, which would explain why it worked for me after making a new character.