I use the same saddle I ride outside on the road. However, I recently tried a saddle without a cut-out and it just made me numb (on the trainer).
Riding the trainer is tough on your "seat." You don't move the way you do outside (standing, leaning, cornering, etc). I teach indoor training classes and combined with race warm-ups can be on the trainer 6-8 hours a week. It gets better the more you do it.
I also find having a bit more padding in my chamois works best on the trainer. I have some shorts with a very thin chamois that I love outside but just can't stand inside.