The advert was run as part of a campaign worth $75m Canadian dollars (£40m; $54m) on mainstream TV channels in the US.
In a post accompanying the advert, Ford wrote that "we'll never stop making the case against American tariffs on Canada".
China's embassy in Washington also used a similar Reagan clip in a post on X to cast doubt on Trump's global tariffs earlier this year.
Ontario is Canada's most populous province and its largest regional economy, and has suffered the most as a result of the US tariffs.
Ford hit back at Trump's earlier tariff threat against Canada by saying he was willing to cut off power supply to the US.
He had also described Washington's trade policies against Canada as having pulled a knife and "yanked it into us", and called on US lawmakers to put pressure on Trump.
Trump's sector-specific levies on Canadian goods include a 50% levy on metals and 25% on automobiles.
The White House's global tariffs - particularly on steel, aluminium and cars - have hit Canada hard, forcing job losses and putting pressure on businesses.
Carney and Ford have not yet commented on Trump's announcement.
It is the second time Trump has said he was ceasing trade talks with Canada, after Ottawa announced it would impose a digital services tax on US technology firms earlier this year.
When Canada rescinded the tax, the White House said Carney had "caved" to pressure from Trump.