He has to be "in" something - a building, a lake, a ditch, a hedge, countless other hidden spots. I'm sure if his body was out in the elements he'd have been found by now.
And so either he was cold and confused, and curled up somewhere for a nap, he'll eventually be found, the coroner will say it's inconclusive (likely hypothermia) and that will be the end of that. I also find my mind turning to the sea having initially ruled it out. Could he have walked and walked and ended up falling/jumping off a cliff or something? Either of those scenarios could mean that literally nobody knows what happened, except Adrian.
Alternatively, someone on that island knows what happened to him. I still think drunken hit and run is a possibility (minus the run, obvs), or an altercation with a homeowner. Perhaps the police need to be asking a very public question about whether anyone has acted strangely these last few weeks, maybe someone who was out that night and could have been in the area. Maybe someone who has replaced a car boot liner or carpet, or someone who has been cleaning something more than normal. Have they asked garage owners and mechanics about any vehicle repairs? Has someone stopped drinking suddenly, or changed their behaviour in any way? Or put the house up for sale or gone on holiday?
Unfortunately, without a body we might never find out as there are too many possibilities. Once he is found things should become a lot clearer.