No, seriously, don't do it. You'll only regret it.
It started off dry, but was chilly -- I think it never got higher than 8 Celsius. That in itself wouldn't have been a big deal, as I dressed warmly, but it soon began to rain. A moderate amount of rain wouldn't have been a big deal either, but it rained hard for hours, and eventually soaked through my coat, gloves, and pants. After a couple of hours I was chilled to the bone and pretty darned miserable. I did bring a change of clothes (no spare rock gloves though), but didn't want to change during the rain, because they'd just get wet too and then there wouldn't be anything dry if/when the rain stopped or we left the quarry. However ultimately I did change shirts because having that soggy shirt pressed against my skin was really awful and I'd been shivering violently non-stop for a couple of hours...and then lucked out because the rain stopped about 15 minutes later. Things were notably better with a dry shirt (although my coat was still soaked through) and no rain, but I never did dry out or fully warm up, only got 'less cold'.
Then there was the mud. There's a lot of dirt in a quarry, and it all turned to mud. This made it more difficult to find fossils, and mud got EVERYWHERE. It was smeared on my face, in my hair, on my glasses, all over my clothes, and when we sat in the car to warm up occasionally, it got all over the car. I had a thermos of hot chocolate, and the mud got inside it, so the drink was gritty and muddy :> Most of the quarry was dull grey limestone, not much colour, so when I found a curious bunch of colourful rocks in this one area alarmingly close to the rock wall (there were several rockslides) I had to go look. One foot promptly sank ankle-deep in quicksand-like mud. Later, because I am not smart, I went back to the same area to look at those rocks again, and BOTH feet sank shin-deep in the mud. That was the only time any moisture got to my socks, because those steel-toed boots were damned good at keeping my feet dry.
As it was, we didn't find a lot. This was our first fossil-collecting trip, and we were obviously inexperienced compared to the other people there (none of whom we knew; they were all from different clubs in different cities. One was even from New York State). One of the best trilobites we did find couldn't be extracted, so I took a photo of it in the rain, and that's why it's a bit difficult to see. Those we did bring home didn't survive the trip in particularly good shape; they flaked off and I don't know how we were to have prevented that. We did bring a lot of stuff home, mostly fossilized shells and parts of trilobites, but nothing amazing like what some people found.
The worst part was that even after we left the quarry and went to visit a friend nearby, I couldn't get warm. I was still cold even in dry clothes and borrowing a vest and blanket, and actually felt pretty sick. Fortunately I've mostly felt better since having a long sleep and taking a ton of vitamin C and raw garlic...although of course my arthritis went nuts starting Monday, and has been difficult ever since. It hates that kind of exertion.
TL;DR The trip was not nearly as fun as it could have been. I could have endured dry chilly temperatures, or a summer rain, but an hours-long cold rain totally sucked. I don't recommend it.
Giant dump trucks
Note that the worker is smaller than the tires, and is wearing a balaclava. It was not a warm day.
Some conveyer belt
I assume it hauls material dumped by the trucks and into that huge pile. It wasn't operating while we were there.
Trilobite
Yes, those are its eyes!
Muddy disaster
My side of the car, with boots et al.
Filthy hands
The mud got into everything I touched.