Cannot tell for sure but if on the exterior of the glass, just grab some Spray-away Glass Cleaner and clean the windows. Nothing to worry about.

Those are alien fingerprints from the aliens that have been peering into your windows at night.

Just kidding.

Not spores, just schmutz!

If it wasn’t the middle of the winter, I’d be wondering if it was some thing alive, but it looks to me like there was something in the wind that hit the glass, and melted and evaporated. It is a bit odd. it could be something from trees nearby that travelled in the wind onto the window.

Put a few splashes of mud on your neighbor's windows and see what they do.

The "trees nearby...travelled in the wind onto the window"????

It could be the start of a Vitricolous lichen colony on your glass. These complex fungus like life forms also develop a partnership with bacteria and over decades can etch and pit the glass. If you've ever seen an old glass bottle laying around for years outside you'll see large colonies on the bottle with a green tint to it, common.

Could also be Iron bacteria that will develop a halo identical to a petroleum spill. It could also be weeping glass disease, (yes it's real) and if you can wash it off, but if it comes back this is what it may be and permanent because it's a defect from the factory.

Bird droppings is acidic and could cause what you see. Little splatters of bird droppings that has nearly washed off can still leave a microscopic layer that can leach alkalis from the glass and cause a halo pattern from light bouncing off it. Tree sap, or any other splatter with an oily makeup can also be the cause, but what I do know for sure it's not spores, and suggest washing it off within the next decade.

Just clean your windows with ammonia OR vinegar, not both at the same time.