It may or may not be the case, I don’t know what Manitoba issues as a ‘temporary’ license, but there’s a world of difference (legally speaking) between a “licensed and a “permit” andif Manitoba only issues trip “permits” you might be better off staying with Ontario license where it’s a 10 day license NOT a permit.
A “permit” is only good in the jurisdiction that issues it, a “license” has reciprocal rights.
I know lots of people ‘do it / get away with it’ but if anything ever happened south of the 49th parallel and you weren’t letter perfect there might be fertilizer on the rotary air circulation device.
The other issue you will encounter is that you cannot cross the US / CDN border with someone else’s personal possessions, even if the Ontario ownership is signed over to you, Customs could care less about a signature on the ownership, its the REGISTERED OWNER that matters.
I’ve been down this road several times myself personally, it’s a bumpy winding road.
