I recently installed the above operating system and have an external harddrive of MP3 and WMA audio and visual files that I wish to use on Open SUSE 10.2. How can I go about this? Is it possible?

You can play wma files in linux too. I don't know which player you want to use, but I'm almost certain that you don't have the codec pack (w32codec-all package) installed. You need it, because most players use the mplayer or the xine engine, and both engines can and will use the above codec pack as default. You will not need to do anything but to install the package. You can download the Suse 10.2 rpm here.

Is there any player you can recommend?

This article may help you.

mplayer (make sure that you download the codecs as well)
http://www.mplayerhq.hu/design7/news.html

Well, I use xine for playing movies (you need the xine-ui package), but my experience says that mplayer works better on suse like distros (and xine is better on debian based ones). For playing music I use audacious, it a simple, winamp2-like player, it uses winamp 2.x skins and has no music library. If you a need a more complex music player (with music library), you should try amarok. Also you can check out kaffeine, its a simple, yet powerful player (plays both movies and music as xine does, and amarok doesn't). The best way to find out which one is best for you is to try them all.
You can also check wikipedia for player comparison. Link here.

Xine works perfectly fine on SUSE. You just need to enable the Packman and Videolan repositories then uninstall the crippled Xine packages installed by SUSE and replace them with fully functional ones from Packman.