That's a trap many fall into. Just asking for "hot roll" or "cold roll" isn't really the whole picture. Pretty much it all starts off as hot roll, independent of the specific alloy. Some you can get either way. HR is generally cheaper, but has mill scale and on most bar is seldom nearly as straight as cold "rolled". This is another minor error. It's properly called "cold finished", since the last process isn't always rolling. On smaller diameter round stock, it's done on a draw bench where it is pulled through reducing diameter drawing dies. No rolling at all. They take hot rolled material, peel the bark off it, and then start drawing it down. Of course, the mechanics of the two processes can and usually do result in different mechanical properties in the finished product, so that may well influence your decision on which one suits your purpose best. That's not the whole story, but most of it.
There is a welding shop here that also serves as a material supplier. Although their prices are a bit high, they do have a nice variety of carbon steel in various shapes, as well as aluminum and a few brass shapes. The guys there vary as to there level of understanding what they actually have. A couple of them are pretty sharp and understand well that if you ask for 4140 cold finish rectangle bar, they aren't going to have it, but can offer a carbon steel in the 1018 to 1026 range, generally. On their aluminum stock, since there are so many posibilities when you consider the possible tempers, they don't even try to stock much other than 6061-T6 or T6511, and not much of that. Can't really blame them though. Most of their customers aren't aware of all the possible alloys that exist. They do pretty well, and are willing to get what is asked for, but in full bars only. Since they are a little high, when I need something they don't stock, I have better places to buy. But I do like the ready availability. They will drop what they are doing and cut it. They have a unique business model too. Years ago, the last sole owner retired, and I think 5 of the long time employees bought him out on equal shares. They have NO employees......everyone you deal with is a partner, so generally other than a grouchy personality of one of the guys.....you get treated well, as long as you know what you want and act professionally.