A machinist once told me that the idea behind stainless steel is that regular carbon steel has very porous oxidization. That means that when the metal starts to rust, the rust can (and eventually will) extend into the steel. Other materials such as aluminum and chrome oxidize in a much less porous manner and the oxides tend to stick to the surface. The idea behind stainless steels is that the surface WILL oxidize, but it will be non-porous and will keep oxygen away from the inner part of the steel. This was a machinist that told me this, so a mechanical engineer may need to clarify some of this.
I don't hunt, so if it's raining, I stay home but, different manufacturers use different types of stainless steel (just go to a large gun store and lay a stainless Savage next to a stainless Remington next to another stainless and you'll see what I mean). I suspect that the level of protection varies somewhat.
That said, I probably wouldn't worry too much about it while hunting, but I would tear the gun down as soon as possible, clean the water out of absolutely everything I could, apply lube and then, if safe to do so, let it sit out of the case for several days. I would also keep it out of any safe that does not have a dehumidifier for a couple days as well, again if it is safe to do that.