The Microsoft Surface RT runs a special version of Windows called Windows RT. The Surface RT has an ARM based microprocessor instead of the traditional Intel/x86 compatible processor used with most other Windows based systems. This different processor requires an operating system that is compatible, hence the Windows RT operating system.
One unique aspect to the Windows RT operating system is that malware written for the standard versions of Windows will not run and therfore won't infect a Surface RT device. In addtion, all apps that are capable of being installed on the Surface RT must be downloaded from the Microsoft App store and contain a digital signature that allows them to run. This is another way in which viruses and malware are prevented from running on the Surface RT. This doesn't mean that the Surface RT is immune to viruses, it just means that a virus would have to be crafted specifically for use with Windows RT.
Windows RT also has a specific version of Defender loaded in the OS for malware protection. Many new malware applications use a flash or java based loader, so you may see the malware attempt to run on your Surface RT but the infecting portion of that malware will not install or run. Defender will likely catch most viruses and malware before they become a problem, again, because they will likely be missing the digital signature controled by Microsoft. To date there is no confirmed reports of a virus or malware infection in a Surface RT.
So why does it appear that you have a virus after visiting an infected web site? It is extremely likely that it is a fake alert from a website wanting you to think you have a virus so you install the malicious code from that site to remove it. This is a social engineered attack that would infect a normal unprotected Windows system, however it would be benign on a Surface RT with Windows RT.
Some people have used Microsoft's own technical site that indicates you do need an antivirus program and that Windows Defender is not enough. However all of the references that relate to this page are for Windows 7 or 8 and exclude Windows 8 RT. Here is the page that is often sighted, read it for yourself. http://technet.microsoft.com/en-us/library/ee692089(v=surface.10).aspx
Like any other computer on your network, you must protect Microsoft Surface units from malicious software. The Windows Defender application (which is included in Windows Vista and on all Microsoft Surface units) is a good first defense against malicious software. But you should also protect each Microsoft Surface unit by using antivirus software.
At the time of this posting there were no antivirus applications available for Windows RT or the Surface RT on the Microsoft App store.
We hope that this information is helpful. Please let us know how this has helped you or if you have additional questions. As always Firestone Technical Resources, Inc. is here to help with your computer support issues - "Providing personal service for your impersonal technology."