OK since we're sharing dead animal stories...
When I took mammalogy in college, my professor wanted all of us to learn to prepare study skins, especially because the university collection was somewhat lacking: mammalogy hadn't been taught since the 70's, and this was 2006. She got some dead test rats from the psychology department, but most of our specimens were collected in the same manner Vorbeau described, from the side of the road. Many smaller specimens were clean kills performed by animals in the care of classmates (when the cat brings you the WHOLE mouse/vole/etc, not just a piece of it).
Anyway, I wanted something bigger than a small rodent, so I chose a big one: a groundhog. It had been hit by a car and its skull was probably broken (thus useless) but while we had several groundhog skulls in storage we didn't have a skin yet.
This is where the gross part starts.
This particular groundhog had been collected by a classmate, and had probably been on the side of the road a bit too long, or maybe spent too much time in a fridge before going in the freezer. Generally, you want them to still be warm, when they're collected. If the fleas are still jumping off so much the better. Now, the way you do a study skin is that you cut the animal open up the belly to the neck, and down to the anus, remove the tail and then the limbs, turn the skin inside out and remove the head. The goal is to do this without puncturing the abdominal cavity, so that you're only removing skin and not muscles or fat. Also, it makes almost no mess if you can successfully keep the organs in and the muscles out. Then the skin is scraped to remove excess fat/muscle/etc, turned right side out, stuffed with polyfill and sewed up at the mouth and along the belly seam. The small bones in the hands and feet remain in the skin (you cut the arm/leg bones as close to the wrist/ankle as possible).
Groundhogs have very thin skin, and I punctured the abdominal cavity. Not a very big hole, but it was clear that the organs were almost mush, and the most disgusting smell came out of the hole. I almost retched, left the room, came back and stuffed it with sawdust and kept working.
The whole experience was like that, and the specimen smelled so awful that I took several breaks, but eventually I got the whole skin removed. This took several lab periods, as we as a class were inexperienced. The prof (it was her first year) had intended it to be only one lab, since it takes an experienced study skin maker only about 1.5h to do even difficult animals like porcupines. Anyway, on a new specimen the skin just lifts away, but I ended up having to run across the whole thing with a thin knife because it was stuck, sometimes puncturing the abdominal cavity again and incurring more blood, goop, and stink. Also poop; the animal died with a full colon (that was THE GROSSEST PART). It took three labs (4h) and a few class periods (1.5h), and even then I only barely got the whole skin off. I'm not doing a good job explaining how disgusting it was, because at the time it was just something I had to do and I did my best, but later her grad student, who was experienced with study skins, finished up the skin with cleaning and stuffing, and told me it was absolutely the grossest skin he'd ever dealt with.
Thinking about it still turns my stomach, even though it was also an interesting experience and I wouldn't mind trying it again with a more cooperative skin! That summer, my cat clean-killed a flying squirrel and I thought about bringing it up to my former prof (I had graduated but was to visit school in about 2 weeks) but I thought my mom would kill me if she found a dead animal in the freezer, even the spare freezer (in a plastic bag of course but still).