Nomadic counties (empty provinces), are always the culture of their liege, and tribals have the settle tribe option.
Culture spread works like this: if a county of your culture borders a county not of your culture, it has a chance to spread, with the MTH being dependent on your stewardship (max 31.67 years at 15), and further decreases if your county is depopulated.
Another method is war - holy wars, most invasions, liberation, and some others allow culture to be converted without the above condition of an adjacent county.
Finally, the easiest method in your situation is if the county has a prosperity of 2, an event with an mth of 40 years can change it for the amount of cash you earn in a year. mth is doubled if you are a vassal, but can be decreased with at least a lvl 3 education in learning, stewardship, or diplomacy, as well as any of the stewardship lifestyle traits, scholar, a "smart" trait (shrewd, quick, genius), diligent, 18+ in stewardship, and finally 18+ in learning.
