Really, really hard.
A conic style instrument, in the manner of a vuvuzela, might be possible by an advanced wood-turner. But a more natural convoluted animal horn-like instrument would be pretty challenging.
I suppose one could carve it out by hand, as long as the convolutions were simpler (no real spirals, for example) but I suspect it would be a lot of work involving clever technique and special tools.
But the shape is not really the important part. It can look like a horn but not resonate, in which case it will not (easily) make a pitch. It needs to resonate as well, which is a function of the how the air space interacts with the "shell".
This can happen more naturally, as in the case of the didgeridoo, which is often made from wood where the heart and pith has been removed (often by termites!)
The comments reminded me of alphorns which are carved from softwood such as spruce. Apparently, these would often be made of naturally curved pieces, but modern design is to fit multiple carved pieces to get the intended shape. So, you could look into the techniques and tools used to make those instruments. In general, you would carve these pieces using typical (and likely custom) carving tools. But each instrument style will probably demand its own special techniques and tools.