Old water spots on a saddle or other leather item won't come out from just oiling the leather or using a leather cleaner. I was told you can't get them out if you don't do it right away ... but I got this method from an 85-year-old man who's been around horses all his life and I decided to try it.
You can definitely minimize the visibility of rain spots, but you have to first open the pours of the leather. Use a regular detergent first ... dish soap or liquid laundry soap (I used dish soap). First wash with soap and water using an old or well used Scotchbrite or other similar scrub pad -- the ones attached to a sponge work best. Scrub GENTLY with circular motion over the water spotted area. WARNING: Don't scrub too hard or you'll strip the color and just exchange light spots for dark ones. (I got two light spots on my saddle from over-scrubbing.)
Once you've gently scrubbed with soapy water, wipe off with damp sponge and allow to dry. Once dry, you can use a small rag to rub oil into the leather. I was instructed to use olive oil, so that's what I did. This saddle was rained on and left untouched for a couple weeks.
Again -- be VERY CAREFUL not to overscrub which will create light areas where you strip the dyed surface away completely. This is certainly worth a try if you can't get spots out any other way. You only risk a couple light spots instead of many, many dark spots.
If you're worried about trying this, then don't try it. I tried it and it worked pretty well but I did get two light spots on the other side of the saddle where I scrubbed too hard. As it happens, I think it still looks a lot better than it did, so I'm satisfied, but will know better next time not to scrub any one area too much.