I imagine it's hard for forests to grow in such a climate

I've been wondering the same thing ever since seeing the map.

No. You'd be surprised. Old growth specifically means forests where the trees are older than 200 years on average. If you include mature forests, which are defined as 80-200 years old on average, the amount of forest becomes much larger. But also consider how much there used to be, and how much disappeared. The US was the first place in the world to really add forest protections. Theodore Roosevelt alone set aside over 150 million acres as national forests at the turn of the 20th century. We're insanely lucky that happened. I've been lucky enough to have traveled to and seen national forests in almost every US state. It makes me die inside knowing they might get cut down now.