I find that I will tear up for a bit and then it will stop (frozen tear ducts? LOL).

When it is really cold, I will wear ski goggles. If you've got enough wind passing over them, they don't fog up but at slower speeds, they will fog up so I put some holes in the foam to try to provide more aeration and reduce fogging. I'm not aware of any bicycle helmets with a visor but e-bike helmets can have them and they also tend to wrap around the head more, providing more protection from the elements.