Handkerchiefs were a commonly carried item by Canadian soldiers in the 20th Century, especially in the first decades, either privately purchased or on issue to troops.  By the Second World War, the handkerchief was seen in Army khaki.  Even at the end of the century, both green and white handkerchiefs are specifically mentioned in Canadian Army Administrative Orders (those taking the training to be military clerks come across a favorite question on exams regarding the issue of handkerchiefs to soldiers sentenced to Detention Barracks.)

A fine example of a unit handkerchief that belonged to Sapper Ted Bishop of the 16th Field Company, RCE.  Bishop's daughter, who donated the photo, adds that the lace border may or may not have been added by her mother!
Photo courtesy Mary Adair