Yes. And I wipe it clean and air dry it afterward. But I prefer not to get them wet if I can really choose. I don't take those delicate ones out when it seems like raining, too.
Yes for some of my leather bags. I drive everywhere so a little moisture does not bother me. Just wide it dry as soon as I get indoors. If I know I'm going to be outside for a long time then I use my Planetes.
Where I live, we have all 4 seasons. I carry my leather bags in any weather and have never had an issue. And I'm really persnickety about keeping my bags looking pristine. The only concession to weather I make is no suede / nubuck in rain / snow.
I don't worry about it. Things happen. The weatherman may say no rain, but you'll get a downpour that afternoon. I must say, though, Dooney all weather leather is the bomb!