I always just put mink oil on my saddles and ride in the rain. They all look fine and are 10-20yo depending which one we're talking about. I condition them with Stubbens Hammanol (use whatever your brand recommends) sometimes. The mink oil seems to do the trick though.
YMMV, but my Stubbens always hold up to whatever abuse I put them through.
I'll echo candysgirl. My tack has gotten soaked multiple times, and I just condition it afterwards. I use Effax Leder Balsam, and my leather and stitching are fine.
The repeated wet leather/conditioning will slightly darken a brown saddle, so if you care about that, definitely get a cover. Otherwise, don't worry about it, just condition your saddle before the leather dries.
I have a 20yo Aramis, a 20yo Siegfried II I just sold to a friend, an OLD 30+yo Wotan and a relatively (compared to my others...) new Roxane. The Aramis is my dress/endurance saddle. I ride in it in whatever weather. The Siegfried II also gets ridden in whatever weather. The Roxane is my foxhunting saddle and I also ride in it, whatever the weather. They've all gotten soaked many times. I condition with Hammanol a few times a year (seriously, I'm really bad about it, its probably 3-4 times a year...) and put mink oil on them probably 2-3 times a year - generally alternating the two. The mink oil does a pretty good job of conditioning also. It WILL darken the leather some, but its always made mine look richer and prettier.
Seriously, I've put mink oil (Fiebigs, the stuff I found at Tractor Supply) on them and just ridden in them no matter the weather. Not one of them looks any worse for the wear, stitching and all. After they get wet, I put them on the stand uncovered (usually they live under covers to protect them from the barn cats more than anything) for a couple days (I will ride them in the mean time) to make sure they dry out completely. The only time I conditioned immediately afterward was when the Siegfried II actually got submerged in an idiot colt meets river incident (apparently laying down was the answer to not wanting to cross...). Its got the toughest leather of the four though and came through it just fine. The Aramis has that cuir crispe leather that is lovely, but probably softer than others, though it holds up fine to endurance rides and getting wet and otherwise abused. I have no idea what the leather option on the Roxane is, but its a fairly soft, supple leather compared to the Siegfried's. The Wotan is pretty tough as well as it was meant to be a polo saddle.
All of them are still perfectly fine and I'd not be embarrassed to ride in any one of them at a rated show.
Erm, rain will not ruin your saddle unless it is made of cardboard. Cows do not melt every time there is a storm. All you need to do if it gets soaked after a ride, is let it dry in an open airy space (maybe take it home of your tack room has temp extremes) and condition it afterwards.
As other posters mentioned, mink oil on it beforehand can help the water bead and shed -- that's what I used on my fireline boots (yes, for setting prescribed fires) to make them waterproof and fireproof. Yes, I did set my foot on fire once with a drip torch, LOL, but thanks to nice oily boots, it rolled right off. See, you can ride in the flaming apocalypse too!
FWIW. I recently got this one because I liked the description that the material stays grippy when wet.
I haven't used it yet, but when I put it on my saddle to make sure it fit (forward flaps), and then sat on my saddle on the stand, it left a pale line down the center of the seat from the interior seam on the cover. Not sure if repeated use will wear the saddle or not, but otherwise it got good reviews at every store that had it and it was recommended in a thread here on COTH.