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It depends a bit on circumstances. In barracks, typically not. In officers' quarters, yes. Outside of the military, it varies mostly based on wealth and the corresponding amount of space available.
She is rather average sized for her race. Humans are the most numerous race in Thedas, but there are also Qunari (who look like Asala, more or less, though the horns come in varying styles), elves (a little shorter and slighter than humans, with pointed ears), and dwarves (significantly shorter than humans and typically stouter).