Protesters against President Donald Trump and his policies have braved frigid temperatures to demonstrate at rallies corresponding with the Presidents Day holiday.

Dubbed "No Kings on Presidents Day" by the 50501 Movement, the latest protests came less than two weeks after a similar nationwide event on February 5 drew participants in dozens of cities. 

Both protests denounced Trump and billionaire adviser Elon Musk, the leader of Trump's new Department of Government Efficiency, an outside-government organisation designed to slash federal spending.

Nearly 1,000 people marched in the snow from the Boston Statehouse to City Hall, chanting, "Elon Musk has got to go" and "No kings on Presidents Day!" 

Boston protesters, some dressed in Revolutionary War-style clothing from the 1700s, carried signs saying such things as "This is a Coup" and "Cowards Bow to Trump, Patriots Stand Up". 

Organisers of Monday's protests, which were focused on state capitals and major cities including Washington, DC; Orlando, Florida; and Seattle, said they were targeting "anti-democratic and illegal actions of the Trump administration and its plutocratic allies."

One sign at the rally, which attracted hundreds in the nation's capital, read, "Deport Musk, Dethrone Trump."

Many demonstrations were slated for cities where temperatures were well below freezing as a polar vortex worked its way across the country.

The rallies followed a series of Trump executive orders and came just days after lay-offs across federal agencies as part of an effort to reduce the government workforce.

With AAP.