I think it definitely counts! You might want to give it a couple degrees of incline to make it more closely match outdoor running, but why else wouldn't it count?
I hate running in cold weather anyway. You bundle up to keep warm, then you warm up and push your sleeves up. I think it's a gross feeling when your skin is cold from the outside but your body's warm from the inside. I had the same problem when I was still skating. My skin would get all red because the cold irritated it but all this heat was coming from the inside.