If everything above is cozy and "woodsy," I would leave the entrance as it is. The stone slabs look very high quality – if it’s really natural stone, better get it sanded down and resealed. It fits the entrance! If it’s more rustic-cozy, I might possibly put up a portiere at the half-stair landing (but definitely made of light-colored fabric!), that would already give the entrance area a cozy feel, and downstairs a tall, narrow floor vase with some greenery, a nice light, and it will look really chic! I definitely wouldn’t paint or do anything over it – if anything, tear it out and redo it. But with the condition, I would think twice about that.