In reality you can train any plant or tree - some take to it a lot better and far easier than others though ;-)

Do you know exactly want type of Willow (latin or trade name) you have as there are many types out there?

Some Willow names and latin examples:

Babylon Weeping. Salix babylonica.
Black-toothed. Salix nigra.
Crack. Salix fragilis.
Pussy. Salix discolor.
Shining. Salix lucida.
Weeping. Salix babylonica.
White. Salix alba.