This crash really has me stumped. If the plane had gone down nose first, I would have expected that searchers should have seen a debris field because the plane should have broken apart upon impact. According to the reports that I have read, the plane fell off the radar shortly after takeoff. Along with that message and considering the weather conditions at the time of the takeoff, I am almost willing to bet that the weather had something to do with this crash. Perhaps, ice or snow build up on the wings and horizontal stabilizer makes sense. Some private pilots expect too much out of their plane's wing heaters and will decline to pay for deicing from a vendor truck located at the airport.
On top of all that, I am also going to guess that because the plane was a small business jet that there were no black boxes on-board or a locator ping unit. This crash is typical of a water crash. Once the plane goes under the water, unless there is a locator beacon transmitting from the plane and no debris field, good luck finding it.
I just cannot imagine why it has not yet been located. Once found, I would not be surprised if they found the plane pretty much together and the passengers still seated.