You cannot take any additional items into the testing 'chamber' save your clothes and glasses. They made me remove my watch and place it along with my wallet and one of my ID's into a safe. For some quirky reason they do allow you to take one state or federal ID with you into the room. I suppose that if the building were on fire and you could not get out a fireman would need to verify your picture ID before rendering assistance.
So the answer is no - you cannot bring in your own writing utensils, even if it is lucky. I would have liked to have had my own as I tend to write big and those sharpen-by-hand pencils they supply get rather blunt ends after a few minutes of scribbling down formulas and diagrams.
Feel free to write down equations and any other information you have crammed into your head only moments before the test. You have an optional 30 minute tutorial at the beginning and it does not subtract from your time. Thus, I recommend that you use this as an opportunity to write information down and take a few minutes relaxing before diving into the DAT.
My test center had rather large partitions between each of the testing stations and they were extended beyond the chair and were rather high as well. The monitor and keyboard were set rather far back and that caused a person to lean forward a little. As such there was no way I could glance over at the person setting next to me so that form of cheating has been effectively dealt with by the folks at Prometric. Furthermore, you might want to bring a comfortable set of ear plugs. While I was taking the exam about six to eight other people came into the room. During my break I noticed that some were taking the GRE, and others what appeared to brokerage or license exams, and so on. Not everyone will be taking the DAT and many of the people in the testing 'chamber' will be furiously typing away on some lengthy essay. Prometric does have headphones to block out the noise, but they are rather tightfitting and tend to hurt after a few minutes. So come prepared with some of your own - preferably the kind you ball up and insert into your ear.
During the break you are more than welcome to write out math equations and proofs, go the little dentist's room, eat a snack, etc. But be aware that the clock is ticking away and if you are not in your seat at the proper time the exam will go on without you. I only took five minutes myself to get up, get a drink of water, and get back to work. On a side note you are required to sign out when you leave the room and sign in when you return. If there are others taking a break with you then that might eat into your time - so really watch that clock.
The DAT is really not that bad of an exam. Just be prepared and those four hours will fly by in no time!