I've lived in Japan for over a decade and definitely not in the foreigner bubble. Cheese is just ubiquitous...

Is it widely used in the countryside, like throughout Hokkaido?

I haven't been to the place, but I'm gonna assume cheese is a big thing there as well, considering 60% of all dairy products in the country are produced there.

I do have been there (I live in Aomori, so quite close), and it's exactly as you describe.

Cheeses (mostly processed cheese) are pretty common food (at least than funazushi) in Japan everywhere at least for 20 years. It seems that lactose in cheese isn't much high.

It depends on your level of lactose intolerance. I have a family member who is lactose intolerant, but can eat aged, hard cheeses.

An aged, hard cheese will have much lower levels of lactose than a fresh, soft cheese, to the point where it virtually disappears.

That can be checked by looking at "sugars" in the Nutrition Facts table: lactose is a sugar, and most cheeses do not have added sugar (well, at least "ordinary" ones). If the "sugars" row is at zero or "traces", that means all the lactose has been digested by the bacteria.

Making milk relevant for all ages is one of the main reasons for cheese existing in the first place.