I was at Orizaba just before thanksgiving. I took way more gear than needed.
For climbing gear, you will need warm boots (i had koflach degres with a mid-weight sock and it was about perfect near the summit), crampons, and an ice axe. a short 30m rope was common to see, but many didn't rope up. you don't need pickets, screws, nuts, or any other climbing gear that i can think of. There was a guide there that i saw with a couple screws and a picket, but never used them; most people didn't carry any. We carried two pickets a piece and a full length rope, some screws, a handful of draws; i wish i hadn't.
weather was probably in the 20's to 30's at the hut during the day and approaching 0 near the summit. We had a bluebird summit day with reasonable but not crazy wind. I'm sure it can get worse. I wore a base layer, a midweight and expedition weight layer and a fleece jacket along with my shells. hat, balaclava, warm gloves. a down jacket might be nice, but i didn't need one.
You can summit straight from the huts, or you can set up a high camp. We didn't summit, 1. because we had too much gear and it slowed us down, and 2. we didn't aclimate at all, which slowed us down. We had to turn back at about 17,700 feet, which sucked, but we're going to go back next year now that we've learned. I think if we'd carried less gear, we would have made it. When you get on the glacier, it seems endless. BTW, we didn't aclimate, because it looked like our intended summit day was going to be bad weather, so we went for the summit on our acclimation day. It was an awesome time none the less, and I'm happy that I was smart enough to make the decision to turn around; a couple years ago I probably wouldn't have done that.