The US military has divisions that specialize in "foresty mountainous terrain". There are parts of the world (and US) that are effectively inaccessible to any mechanized units and the US military has large combat units that are setup to operate effectively in those environments. Terrain that is prohibitive to mechanized units is traditionally the domain of "light infantry" divisions (e.g. 10th Mountain Division), distinct from mechanized infantry divisions.
The US military has dedicated units and training facilities for virtually every environment on Earth.
The US military has dedicated units and training facilities for virtually every environment on Earth.