two ways this would be possible? the UI method mentioned above, or a particle system.
The ui method is most commonly used. its basically putting a animated 2d image directly in front of the game camera. The main downfall is that it would also appear indoors, unless 343 implemented some kind of system that detected if the area a person was in was pretty much closed off. which i cant think of any way that would be possible.
The particle system method is different. It emits individual planes of polies for, say, snowflakes or rain drops. this alters performance MUCH more. The only way to not make it work indoors would to place colliders on each flake or drop, which would destroy the framerate even more.
Lightning isnt very hard, just a bit of cool lighting effects.
So yea, thats about it. if they did this, they would most likely have to use the Ui method, somehow.