Is the gender of the Holy Spirit, feminine or masculine? I know the Holy Spirit (רוח הקודש) is usually referred to as masculine. But, what is the reason for that?

The Hebrew word רוח (ruach; "wind; spirit") is one of the few words that is sometimes used as masculine (cp. Eccl. 1:6; 1 Kings 19:11), although it is mostly used as feminine.

In other Hebrew literature, such as the targumim, the Shekhina (שכינה), which some believe to be the equivalent of the Holy Spirit, is also feminine.

Therefore, I find it questionable that all the persons of the Trinity are considered male in gender. Personally, I think connecting more to the feminine side of god can lead to a softer and more understanding and open approach, whereas connecting too much to the male side might lead in my view to a judging, hard, and maybe sometime, even aggressive religious approach.

This place seems to agree with my observation: "Gender of the Holy Spirit"
The Hebrew language only has two grammatical genders: masculine (זָכָר) and feminine (נְקֵבָה). Therefore, every Hebrew noun has an inherent grammatical gender. In the case of the noun רוּחַ, the grammatical gender is feminine. Yet, this does not mean the natural gender of the Holy Spirit is feminine. As for why the Holy Spirit would be "male," so to speak, it is because the Holy Spirit is the Spirit of Yahveh (Jdg. 3:10), and Yahveh is a He. I say "so to speak" because Yahveh is "male" in a different way than animals, which are determined to be male or female based on their chromosomes. Rather, Yahveh is described as a male, in part, as a consequence of His headship over all creation.