Oil is the primary money making industry for Saudi Arabia. With lower prices, of course it makes sense that their economy would be in financial turmoil. Their oil is their most valuable resource and asset. Without that, they do not have much anything else to use to help their economy.
The Saudi economy relies very heavily on its oil rich assets. The good thing they have going for them is that they are very well aware that the price of oil is quite volatile. But it does look like oil is not going to return quite where it was in recent years. I'd expect to see the Saudi economy take a hit and they could experience a bit of recession if this trend sustains for a long period of time.
The Saudi Arabian economy is not in financial turmoil merely because of falling oil prices. The country still produces oil very cheaply. There are larger symptoms, including an oppressive regime and a government that overspends in order to maintain its power. This will prove to be unsustainable in the long-run.
No, the Saudi Arabian economy is not in financial turmoil because of falling oil prices, because the country has a lot of money in reserve. The Saudis would have you believe that they are in dire straits because they don't want you to feel bad about paying high prices for oil. But it's all a gimmick.