I am traveling to Madrid at the end of march. what is the weather like there and how should i dress accordingly? Coat, light jacket? Is it warm enough for skirts or sandals?

Don't trust the temperatures of these week. Although these days you can go just with a light jacket during the day or just a shirt in the sun, this can change from one day to the next and you could need a coat again. Nights are still a little bit cold. It's not hot enough for sandals yet in my opinion. You better bring several clothes by levels that you can keep on or take off.