Leather was once worn by a cow who stood around in the rain and we compete and hunt in rain. It won't hurt it.
But leaving it out in direct sunlight, in a hot car/trailer or jammed in a trunk when it's wet sure will.
Just towel it off and let it dry out of the sun and away from any heat source. Give it a light coat of oil or conditioner. Any spotting will work out with use and oil or conditioner given a little time, don't over condition trying to speed it up.
It'll be OK.
When opportunity knocks it's wearing overalls and looks like work.
If my old Passier can survive years and years of hunting in the PNW with all that rain and occasional dunking in the Fraser River, yours will survive just fine. Dry it slowly out of the sun, and condition, as per above.
Proud member of People Who Hate to Kill Wildlife clique
I once had someone make a cake for Mr. Larkspur's birthday party. The cake lady suggested decorating it with a mountain scene and I agreed. I had to suppress my laughter when I picked it up -- a large sheet cake with white icing and a huge blue oval spread across the top. At the edge of the blue oval was a blob of green icing and a little plastic rock and plastic mountain lion.
It rained, so we all went inside and left the cake out in the rain.