...of course any device is subjective to malware and virii, however, I do not believe that for closed-market devices such as the NOOK, antimalware software is required.
Because the NOOK devices are served with applications by Barnes & Noble's own Appstore, where apps go through a lengthy test-process before they are provided to its users, chances are minimal for bad applications to pass through. Unlike Google Play, and similar as Apple's Appstore, developers have to go through a similar lengthy process in order to be accepted to create applications that will run on the device. With Google Play, anyone with $25 can create whatever they want, and publish it without fear of rejection. A lack of quality control is both the Play Store's greatest power and its greatest weakness.
However, part of the popularity of the NOOK devices is the ease of which they can be modified to run a stock Android version, which does not have the restrictions of the original NOOK's operating system. By breaking the NOOK free from its Barnes and Noble chains, its users are of course subjective to whatever is available in the, uncontrolled, Google Play market, and as a result are more subjective to whaver malware it might have in some of its applications.