You could do that in smarty as well as in css.
For smarty, you would be needed to give the condition that if it is not in the order page, display it.
For css, you could provide the id of the page and the id of the column to be display: none
For example,
order is the id of the page
left_column is the class of the div which you want to hide..
you could use #order left_column {
display: none;
}
Smarty is the good way though..