Just wondering what rod would be best to use hot rolled or cold?
Others have suggested a steel to use. I'm not going to do that for you but perhaps I can add a perspective.
The low torque used to tighten a drawbar results in a correspondingly low tensile stress in the drawbar that almost any steel can easily handle. If I were making one, I wouldn't be very fussy about the steel I used.
Because a drawbar gets frequently tightened and loosened, I'd be much more concerned about the quality of threads I cut and the resulting fit and wear conditions imposed by repeated use of collets and arbours on poor quality drawbar threads.
Another condition to be aware of and perhaps design around is drawbar rattle. To have the best chance of being rattle free, a drawbar has to be held in the very center of the quill. If it is not centered, centrifugal forces can play havoc on a long spinning shaft. A fairly effective solution is a centering bushing. But this isn't always as simple as it sounds. Many factory drawbars have rolled threads which means the shaft itself is smaller then the OD of the rolled threads. To address this issue, the bushing ID has to be sized to fit the shaft and then inside threaded to fit the shaft threads. The bushing is then installed by threading it over the drawbar threads and then sliding it to the top of the draw bar.
Here is a picture of my bushing. It is inside threaded to fit the drawbar threads and the smaller OD of the collar fits the ID of the top of the quill. The ID of the bushing fits the OD of the drawbar shaft.
Here is the thread I posted about this bushing. Your drawbar might not need to worry about rolled threads, but it is likely that your quill ID is bigger than your Collet threads.in other words, you will still need the bushing but it won't need to be threaded.
Thread 'Draw bar rattle'
https://canadianhobbymetalworkers.com/threads/draw-bar-rattle.4258/