I have an ENO doublenest for winter and a grand trunk that is a single for the summer when it is hot. I camped 3 nights at shamrock and just had a light sleeping bag and the ENO ember 2 under quilt. I have a zero degree down under quilt from hammock gear that was stupid expensive, but man that thing feels like it makes its own heat.
The week before christmas, I camped in Big Bear, California and it was 9 degrees actual with 15-20 mph winds and snow. I literally had the best night of sleep I have ever had in my life.
As others have said, it is just important to get something under you for insulation, even if it is just a foam pad. The ENO under quilt is cheap and I recommend it.
Regarding the tarp, I have an ENO profly, but I wish I had bought the profly XL. They do great at knocking the wind off. They also keep the dew off and block the morning sun as mentioned. I don't always use it. With the down under quilt, it is a must though. Down has a natural odor when wet and the dew is enough to make that under quilt smell funky. I can't handle it, so I always use the tarp with it.
I want to try the asymmetrical hammocks as mentioned, but my problem is that I am already so deep into this thing with the down under quilt that I can't change directions now. I would also really like to check out the warbonnet blackbird. It is a bridge hammock.
As far as setup, I like a very flat hammock so I stretch mine as tight as it will go and then get in it. I try to keep it level as well. Some people say leave your feet high, but I can't handle it. Level or feet down a little is best for me. The big thing is just finding what works for you. Flat works for me.