Water damage indicator on, iPhone still working

I dropped my iPhone in the snow (obviously picked it up right away) and it is still working fine, but the water damage indicator at the bottom is red. Everything I've read about water damaged iPhones stresses the importance of not trying to turn the phone back on, but mine never turned off.

Now I'm scared that if I do power down or plug it into my computer that it will short circuit. Should I take the risk of turning the phone off and going through the motions of attempting to dry it out (put in a bag of rice, etc) or is it possible that just enough moisture to activate the water damage indicator got in and left the actual phone unharmed? Thanks.