I’d like first to enumerate some terms defining how the women are covered, in order: headscarf < hijab (you saw the whole face) < chador (the extension of the hijab to cover the whole body until the toes, usually black) < niqab (you saw only the eyes) < burqa (the whole face and the whole body is covered)
In Iran, as an Islamic Theology, a basic coverage is mandatory by law for all women of any religion. In Egypt and Jordan, a western Woman does not have to wear any scarf. In Iran, she has to. A special police department takes care that the rule is applied, firstly for the Iranian women. Those women not respecting this law get arrested and go to jail; I saw such a police movement! Indeed, many would wish not to have any obligation! Fortunately, the private sphere is respected, the rule mostly applies in public areas; at home, my CS hosts in Tehran (and their place, a fully equipped flat with washing machine and dishwasher) were pretty like in Europe.
You do see a lot of chador in the city, especially in the bazaar. But the majority wears only the hijab or just a light headscarf to cover their head. In some more liberal areas, the headscarf is not even completely covering the head: you see the front and some hair above.