Removing Water Marks on Windows

What you are describing as water spots sounds more like Sticker spots. Sticker is a chemical that somewhat water proofs another chemical like fungicides. The make-up of this stuff is pretty simple it's like Elmers glue and dish soap, something I have used when landscaping in large complexes.

To remove Sticker spots use alcohol, rubbing will work as will alcohol based hand sanitizers. You may also have to use a light abrasive like baking soda. Dampen a cloth with the alcohol or rub the sanitizer on the window and scrub ( you may want to let the sanitizer sit to work it's way into the stains) then polish with the baking soda and rinse. It may take more than one application to remove all this stuff.

After you get the windows clean seal the glass with a rainex type product. Also check into having the golf course clean up their mess, if this has gotten onto your windows via a pesticide application they could be liable for the damage.
I do not think there is any health concern as a Sticker product in not used with toxic chemicals.

Once you get them clean, coat them with Rainx. It will save a lot of work later on.

You could try using a window cleaner called Invisible Glass. You can find it in the automotive section of most supermarkets or of course at auto stores. This has taken a lot of tough gunk off of our windows.

Try a Magic Eraser on one, and you may be able to get the build-up off. You will probably need to follow up with Windex or another glass cleaner, but hopefully they will do the trick.