Logout sleeping pose is kind of weird and overly straight, but his tail is flat underneath his legs. He sits down on it then shuffles over, putting weight on his hands and feet. Logging in again, he's already sitting up but still seems to have his tail
clipping through the bed underneath him.
Default /doze position... on his side, never mind the horn going straight through the pillow! It could work with a thick shaped pillow that has a slit in it, maybe.
Also makes me notice that the scales on his neck seem to come to a sharp point right where it would dig into his throat when looking down...
Doze 2 - on his stomach, head resting upright on hand. I tried lying down like this and as soon as I relaxed, my head was leaning over against my left shoulder. Still, probably necessary for anyone with the more backwards-pointing horns, and they would probably also help to 'prop up' the head somewhat.
(Would also probably put the pillow under his chest when it's not welded to the top of the bed like it is in the game.)
Doze 3 - on back, with leg raised so the tail can lie out to the side. Makes sense for my character, and probably works for most horn shapes besides the really backwards-pointing ones (as there's still space between his horns and the pillow) but would be very dependent on their secondary horns! Obviously not going to work for the default hairstyle from the examples I posted earlier.