There are a lot of coops built on the ground with just a dirt floor. It's been done that way for a looooooong time. But, and it's just my opinion, unless you are building some massive coop for a hundred birds or so, a raised coop with a wood floor is the way to go. Unlike a coop built on the ground, you don't have to mess with building a serious foundation. My coop is 8X16', and it is sitting on top of 6 sets of concrete blocks, leveled into the ground. I didn't have to mess around with mixing concrete, and making a foundation. If some of the blocks start settling into the ground, I'll just jack up, and shim to re-level. Also, with a raised coop, The birds have a nice shady place to hang out, on sunny days. With a raised coop, if it snows, I can still easily get into the coop without having to clear any doorways. If you build a raised coop, just make sure you raise it high enough, so you can easily see whats going on under there. As I said before, you don't want to provide any hidden spaces for pests.
I don't know where you live, but hot summer days are more of a threat to chickens, than winter cold. I get temps here, in the winter, down into the single digits, not including any "Windchill". The front of my unheated and uninsulated coop is wide open, covered only with hardware cloth, and the chickens are totally fine with it.