I use my iphone for music streaming and/or my own library, and also sometimes to look at my data when I'm using the Kinetic app. Depends which "toy" I bring on my trainer.

I don't sweat that much, at least not on my phone.

There are various options you can look at, like a phone case
Topeak has a waterproof one http://www.topeak.com/products/bags/..._drybag_ip5_bk (which I have) but using it in the sun can be an overheating problem. But it works well for me in the basement (I slit opened it as I could not find the non-proof one at a decent price).

But what works well for us is a ipad/toys like remote, etc holder on a tripod. You can make one at home very easily with either a camera tripod and getting the adapter or a DIY version out of wood. We have both and they work great and you can see/access everything at a glance/touch of finger as it is right in front of your wheel (trainer).