We had one of our boarders horses die in it's stall one night, and we didn't learn about it until late the next day. I had to disassemble the front of the stall, get a strap around the horse, and drag it out of the stall with my tractor. Took me about four hrs to do the whole thing. It's something I'll never forget. Next time I'll just burn down the barn.
My neighbor's mare died while birthing a foal (and thefoal died too). My husband had to help him dismantle the side of the stall and then remove the exterior door of the adjoining stall and then haul the mare out into the open in much the same way you describe. (The vet had already taken the foal to his establishment in an attempt to save him.) It was an all day job. I don't remember it smelling, however. It was still cool (Wisconsin) and the horses had not been dead long.
I just remember that my neighbor (a man) was sobbing at the loss of his brood mare and her beautiful foal.