Hyundai Repair: Gas smell in my Tiburon, rear quarter panel, 2005 hyundai tiburon

Question
I have just recently noticed a very strong gas smell when I start my car. A 2005 Hyundai Tiburon V6. It is sometimes worse than others. Today I stopped by a mechanic shop and he checked everything that he knew to check and said everything looked fine. He didn't see any signs of leaking fuel lines or fuel filter or injectors. I  I told him that I had noticed a couple of days before a small hose dangling off the back underneath part of my car. It looked kind of decomposed and it had ice inside of it. (its cold here) It was dark and when I touched it , it fell off. I looked at it because I thought I heard something dragging. One may not have anything to do with the other. Anyway if you have any ideas I would sure appreciate it. My dad can check it if he knows what to check for. Thanks a lot  

Answer
Most likely, the fuel odor is coming from the exhaust because of the richness of mixture required to run the engine at very cold temperatures.  This is suggested by the fact that you report smelling the odor only when you start the vehicle, but not after it's been running awhile.

You might stop by the dealer and have them check as well just to be safe.  Providing there are no leaks in the fuel delivery and the evaporative system, the dealer may also check to be sure that the mixture is being properly controlled, which will require a scan tool.  If there is an issue it should be covered by your warranty as long as you have less than 60,000 miles.  

There aren't many hoses on the rear of the vehicle.  What you saw may have been a drain hose for the sunroof (if you have a sunroof).  Usually, such a hose would come out of a rubber plug in the inner panel of each rear quarter panel and just inside each front fender below the front pillar.  The former should be reasonably visible.  The latter will require disassembly to see.