The phrase "birch bark" likely brings to mind white sheets of loose bark, like that found on Paper Birch, but some birches have outer bark that is neither white, nor exfoliating.
Cherry Birch (Betula lenta) has dark bark (the species is also known as Black Birch), accented with horizontal dash-like lenticels, or breathing holes, through which the tree can exchange gases with the atmosphere. Young trees (above) start out with mostly smooth bark, which over time develops vertical cracks. These stretch marks become more numerous as trees age, eventually leading to bark that breaks into thick plates (see the progression in photos below).
In winter, aside from examining the bark, look up to see the twig pattern of Cherry Birch. Notice how on older twigs the leaf buds occur atop a stack of leaf scars that form a sort of spur branch. If you find a tree with twigs you can reach, you might try nibbling on one to enjoy the wintergreen flavored inner-bark.
Note that Yellow Birch (B. alleghaniensis) has similarly flavored inner-bark but can typically be told from Cherry Birch by the presence of exfoliating, lighter-colored outer-bark (though young trees can be similarly dark-barked). Luckily, a twig of either species makes a pleasing trail nibble.