Hi Shadow,
It might have something to do with the keyboard. Technically you are not splitting the desktop, but a window. I only mention that as I want to make sure I am understanding the issue.
For example - if you open a terminal on a blank desktop Mod-Enter - then hit Mod-H - then Mod-enter again you should get two terminals horizonally arranged. Then depending on which one is focused you can then hit Mod-V and Mod -Enter again and that window will be vertically split, etc...
If you want to try different key combinations, go to your home directory in PCManFM and go to the "view-show hidden" menu, or hit control-H and you will see the hidden .dot files. Open the .i3 directory and there is a plaintext config file that has all the keybinding that you can change to whatever you like as well as things like startup programs, etc.
Another interesting thing is if you have a couple windows on a desktop and they are arranged vertically, you can alternate between horizontal and vertical by using the Mod-E key also for open wndows.
enjoy....biff