How can I create a white list of a server that distinguishes between Mobile devices based on their UDID.
This depends on what service(s) you have on that server and what protocols you are using to access those services.
Assuming that what you are talking about is a web server though then you are unlikely to be able to do much that will work for mobile devices in general although the amount of data that is leaked in this way is quite scary for some device\provider combinations. Typically the relevant identifiers are not actually provided by the client browser but by the cellular provider's internal proxy\gateway infrastructure that often takes quite an intrusive approach to things like http traffic. Colin Mulliner, a security researcher who concentrates on mobile tech, had a nice presentation on this from CanSecWest earlier this year that you can download from his website.
Some other services that are aimed at mobile platforms (Exchange Push mail springs to mind) provide for whitelisting based on hardware device-ids but it isn't very common. In most cases it is just one of a number of security mechanisms, relying on this identifier alone isn't advisable.
If you are building your own services and are in a position to write functionality for both your server and client systems then it's not that difficult to leverage device-ids as part of your overall solution but you will have a lot of development to do if you want to support more than one client platform.