Salam
Yes the Hanafi madhab does exist in Saudi Arabia. Here is a picture of the renovated Shahlubiyyah madrassa located in the al-Koot area of Hofuf. I will try to post some more information about the history and age of this school. Regular lessons still take place here in the evenings, books such as al-Hidayah and Mukhtasar al-Quduri are currently being studied. There are also lessons teaching other smaller works on the Hanafi madhab. Sheikh Yahya al-Mulla along with some other Sheikhs from the al-Mulla family teach here.