A tuque is indeed a hat which keeps us warm during
the -20/-40 winters of Québec and the rest
of Canada. The word "tuque" is especially used in other, metaphoric
expressions as well.
"Attache ta tuque!"
This expression means "you'll have a hard
time doing this or that". Another variant
"Attache ta tuque avec de la broche!"
That means the task at hand is even steeper.