I have taken mine in the shower with me once. It was alright.
They seemed to be fine with the water. It was one of our FEW cold days here in Sunny Florida

and I just closed the bathroom door to help keep the heat in.
I sat on the "floor" and soaked them down and then lathered them up. I did pick them up and hold them to rinse them. That was easier. I do not think I would hold them while trying to get the soap all in and worked up. I would be afraid of them sqirming and falling.
Did not get any scratches though.
Will probably do it again this weekend since it has decided to be cold a little more.
I envy some of you who have such cute jackets for your babies and actually NEED them. I do not think I would be happy where I could get snowed in but a little snow would be nice for all my kids (skin and furry) to play in. Will just have to be happy with frost and the pictures on the TV for now.