Coyotes of Yosemite are beautiful animals, not the somewhat mangy character you see down at lower elevations. They are also probably a bit overabundant. Unlike bears, they don't tend to eat a lot of our food directly, though they easily become inveterate beggars and must not be fed under any circumstances. More commonly, though, they get food from us in a secondary way. Our habits lead to huge increases in the ground squirrel populations which makes for easy hunting in many places where people are common. In addition, like the ravens, coyotes enjoy a delicious meal of fresh or not so fresh road kill.
Despite that, they are fascinating animals, active all year long. In the winter, it's quite easy to track coyotes and I have followed their tracks for miles. They will just stick to the line of march, varying by only a few degrees left and right unless they see a hapless squirrel and decide to make a dash for it. They use our roadways in the winter to facilitate their hunting. The high snow banks that trap squirrels in the road bed and coyotes will often cruise the road for miles. You'll also see coyote tracks in the forest, loping along presumably trying to catch a short-legged squirrel foundering the snow. Because of that, a few inches of snow is good news for the coyote. It slows him down little, but impedes progress for the squirrel dramatically.
Two signs that you're following a coyote rather than a domestic dog are: 1) the coyote track doesn't wander aimlessly like Fido who has been stuck inside all day. The coyote is down to business and sticks to plan. 2) the coyote always puts his hind foot in the same spot as the forefoot was. He is an incredibly efficient snow traveler because of this and, again, the well-fed Fido is too distracted by the outdoors to worry about such minor efficiencies.
You can also watch them in winter in the meadows with their heads down, listening for little guys scurrying about in the subnivean layer. The coyote pauses, crouches and then leaps in the air in an arc, coming down jaws first, peircing the snow and hoping to come up with something other than ice and grass in his mouth.