Fair warning, I’ve never sampled cotton in my life. As best I understand, this is how it works.
Stab your knife into a bale of cotton. Use the broad tip to scoop out a sample. Trap your sample between thumb and ricasso. Pull the cotton as though you were spinning it. The way the sample stretches, and the number of times you can wrap it around the ricasso, tell you about the quality of the bale.
My experience with sampling is nill, although as a kid I had some limited experience with producing and selling it. Cotton was already on it's way out as a big crop when I was in my early teens, but I did get in on a few crops and learned how it is grown in the US. The hard part is growing it.
The fun part, for me, was harvesting it. Before I was old enough to be trusted with operating heavy machinery, I was paid to "tromp cotton" in the cotton trailer. The cotton is dumped from the cotton-picker into a trailer with tall meshwork sides (about 6~8 feet high) and my job was to jump around in it to compact it as tightly as possible before the next load was dumped. I'm sure I wasn't the first or last kid who thought that was the best paying gig ever, for the first day or two anyway
The filled trailers were taken to the cotton-gin, where the raw cotton was cleaned and compacted into bales. It was baled twice: into "rough bales", and then later into "finished bales". The difference between the two was the degree to which it had been cleaned, and more importantly, to which it had been compacted. The rough bales weighed about as much as the finished, but took up not quite twice as much space. A finished bale is roughly 2.5 feet wide and high, and around 4.5 feet long, weighing in at 500 lbs or more. It's compacted to nearly thirty pounds per cubic foot, and believe me, that's pretty darned tight.
I never saw any sampling take place, but as a kid my interests were on other things at the time. However, I did run around with friends in the warehouse where the bales were stored, and can tell you from experience that cutting into a rough bale was a daunting task. Like attempting to stab baled, compacted cardboard, it took a lot of effort and multiple attempts to get a knife worked into it, and once we did, it was hard to pull any of it out.
I can't imagine how anyone could sample a finished baled without power tools. That cotton was so tight, it was comparable to mdf (slight exaggeration for effect

). Farmers before the advent of modern machinery were definitely made of stern stuff, and this is just one example that might show it.