From the Transports Quebec website:
"What is the definition of winter tires?
The regulation, adopted on September 17, 2008, and which will be published in the Gazette officielle du Québec, defines tires specifically designed for winter driving as those that meet one of the following criteria prior to December 15, 2014:
Tires on which one of the following inscriptions appear: Alaska, Arctic, A/T or AT Blizzard, Ice, LT, Nordic, Snow (but not mud and snow), Stud, Ultratraction or Winter
or
Tires on which the icon representing a mountain with a superimposed snowflake appears."
http://www.mtq.gouv.qc.ca/portal/page/portal/grand_public_en/vehicules_promenade/securite_routiere/securite_conditions_hivernales/reglement_utilisation_pneus_hiverSo, I'm assuming your new tires do not have the Mountain & Snowflake symbol. If that's the case, then it looks like you're out of luck.
Depending on the size and construction, some of the Motomaster Total Terrain A/Ts do meet the regulations (LT sizes), but yours (P-metric) do not.
Seems kind of arbitrary, but that appears to be the rule.