Translation:The tired man gets off the horse and goes into the bathroom.
Mosdó can refer to a room in which there is washing-up stuff and toiletries, or it can refer specifically to a sink.
WC or vécé can refer to the room with the toilet in it, or to the toilet fixture itself.
This discussion always gets more confusing because depending on where you are in the English-speaking world, "toilet" may refer to the room or may refer only the actual item.
(I think that's all correct!)
Also, fürdőszoba is a room where you have bathing stuff (but in a large, modern one there's probably also a toilet there.)