It's generally agreed that the hijab is to cover a woman's figure, hair, neck and ears. To what extent depends on which school of thought you choose to follow. In my opinion, the scarf is not the only way to cover the hair, neck and ears although it seems to be the easiest I think its good to experiment with other things!
For example, a winter hat and scarf set would be a perfect substitution when going outdoors on a cold day where you won't need to take them off e.g. shopping, walking etc. Here are some photos to inspire you :)