In my experience, coyotes are a factor on fawns and adult deer in dire situations (starvation, deep crust-topped snow, wounded, etc..)

A few things to note though.

Finding a deer torn apart from coyotes does not confirm a coyote kill. The deer may have died for various reasons and where found by the yotes, or the yotes finished the job. Certainly happens during hunting seasons and on roadkills. I am not saying its impossible for deer to be killed by yotes, but a carcas w/ yote prints around it is not proof that a yote killed the deer.

Also, Deer are not 100%defenceless to coyotes. Ionce saw areal angry doerun off a coyote mother and three pups that found her fawn. Granted that was not in winter conditions.