In order to master this game you have to strategically choose one lucky sheep to survive them all.
I found that if I let my facade of a human soul slip I could keep the game going indefinitely by just letting one sheep enjoy the fire rather than keeping them all in. Since the stakes were high since the start (all the sheep ran away ASAP) I did not care for trying to recover them all since the difficulty of doing so would mean immediately losing the game.
I think if you were to keep working on this, having the sheep leave in stages, slowly building up the chaos of the player having to manage them all, it would have a much greater impact on the player since they can get a hang of the gameplay loop ( and also bond with the sheep ).
While the main concept is simple, having an extra mechanic to let the player finely control or predict the behavior of the sheep could be a great way to add some skill threshold on top of the existing arcade-esque gameplay, rewarding players with a keen eye, or with proper preparation.
Dare I say maybe giving sheep some sort of upgrade that let them behave differently, e.g. This sheep will attract other sheep to itself when it runs, or something like that to give the player something to work with and characterize their sheep to make the gameplay more interesting.
Overall I liked what I played thus far, great job! (Also, I liked the throwing wood mechanic, more of that plz!)