Might sound like a random question, but does the hood roll or fold up into the jacket at all?

Yes. Their are Velcro tabs to facilitate folding the hood on my jacket. Also regarding sizing. I’m the maximum of medium size on their sizing chart. You may want the next size up if you want to layer under the jacket. I do like this jacket.

Would this be a good jacket for very cold weather say 30 degrees or less?

I've had the Rothco version of this (well many of them, I buy one every other year), I use them for winter bike commuting in Northeast Ohio. They do not work as a stand alone jacket at that temperature but they can't be beat for wind/rain/snow protection and rugged protection from scrapes and falls at this price. Buy one size too big, then add layers. I use a wicking baselayer tech tee or bike jersey, my regular clothes, then an insulated non-water/windproof hoodie with face mask built in, then this shell. I've been comfortable down to 5-10F (with appropriate gloves, socks, pants, etc).

waterproof or water resistant?

Hi. I purposely wore mine in a downpour for 1.5 hours. I had treated it with Granger’s spray. I was dry. You may want to carefully consider sizing choice. I’m close to 180 C.M. tall and 180 pounds. I wish I had purchased a large so I could layer under the jacket. Mine is about 2 years old and holding up fine.