What being tall means to me
Yes, height matters to women, especially before she gets to know you. Usually, women have a fantasy of being with a tall man, especially a man who is taller than her. Even if she is 6 feet tall she still would prefer a man to be taller than her. But...it's only for first impression before she gets to know him.
Women want attractive man, they want a man who they are attracted to, but attraction is not always a choice.
A woman can say she likes men only 6ft and taller but then she could be surprised when she gets attracted to much shorter man.
Yes, it's possible for a woman to get attracted to a short or much shorter man. Such attraction can happen unexpectedly for both of them though.
Height does matter
Most women, not only tall women, dream about a tall man. Very often even women who are only 5'4" tall dream about a man to be at least 6'0". So, most wouldn't want to go out with a man who is only 5'5" or less, unless she knows something else about him than just height and looks.
Once a woman gets to know more about man, then height isn't such a big priority anymore. Height is very important only for first impression. For example, tall women prefer tall men because they often assume that men want a shorter woman.
From my own experience, since I'm so very tall, if I met a man who is 5'8" tall, I would wonder if he finds me attractive at all, because many men prefer a shorter woman. If I find out that he likes even that I'm 6'0" tall, then I'm very likely to like him back too. Women could find a certain guy interesting, but to know if she is really attracted to him can take some time. If you are a guy, touch her and she if she likes it.
Height and other qualities
If you are a guy and you really worry about your height, it's better to stop worrying about. Better to focus on other much stronger qualities that attract women. More women care more about money, social status, popularity, if you can achieve all of those, it won't be a problem to find a woman.
There is not much you could do about height, but you can improve how you dress, groom yourself, develop interesting and attractive personality. Did you notice how some people just attract others like magnets? So, there is much more to attraction than height.
Women can say that height is important, but if you have something else that makes her feel even better about herself, then she will go for you.
Women like tall men because it makes them feel good and feminine. If a woman is taller than her lover, she might feel too masculine, unless he has dominant personality or other qualities she is very attracted to.