In general pine country is where pine or evergeen trees grow and is different than where broad leaf or deciduous trees grow. The climate for pine trees tends to be colder and drier and therefore less inhabited. The needles stay on the tree year round since the small leaves and waxy coating restricts evaporation during dry winters. Deciduous trees will drop their leaves before winter.
The writer is referring to an area which is more desolate and harsher and colder (further north), painting a morbid scene in which to kill oneself. The passage takes place in Akron, OH. The native trees of Ohio are deciduous, so the author is probably talking about travelling much further north, maybe into Michigan or further into Canada.
Pine trees can also be found naturally in southern areas for example Georgia Pines but they are much taller then their northern cousins.
Tree environment is also distinguished by mountain elevation where evergreens will be the only trees to grow above the snow line.