Yes, I hate showers. I only take them because I hate being dirty more.
One thing you should do is get a shower head that comes attached to a hose--you know, the kind that you hold in your hand and point away from you when you turn the water on, while you get the temperature right. That way, you don't have to deal with the cold water, except for it splashing your feet and your hands, until you get the temperature right. It's easy to install, too; you just unscrew the old, fixed shower head and screw the new one on.
Have your towel within reach. Dry off while you're still standing in the shower, if it's big enough that that's possible, or immediately after you step out. The faster you dry off, the faster the cold, wet feeling goes away. You can also dry your body with a hair dryer after you dry with a towel, if the damp feeling is too much for you.
Maximizing your efficiency is a way to make your shower as short as possible. Always wash your body in the same order every time, make it a routine that you don't have to think about, so that each action reminds you of the next one. If you only have to spend five minutes in sensory purgatory, it's much more bearable.
Short hair helps. You spend much less effort on washing it. If you're a guy, or a girl and don't mind looking a bit odd, a buzz cut is probably the most convenient haircut of all. You would probably have to get used to the feeling of air on your scalp though. I always notice that for the first few days after a buzz cut, but not having my hair brush against my forehead and neck anymore is such a relief that it's worth it for me.