Mr Trump's decision earlier this month to become the first sitting USA president to attend the event since Bill Clinton in 2000 has prompted widespread head-scratching among numerous other 3,000 participants of the four-day talking shop on everything from tackling climate change to the rise of cyber attacks, corporate greed and sexual harassment. Apart from Trump, many heads of states including India and the United Kingdom are in Davos for the forum.
Pressed on whether the gathering - known to attract the so-called "globalists" derided by some factions of the Republican Party - aligned with the president's populist economic rhetoric, Chao defended the summit as a unique opportunity for world leaders to gather and exchange ideas.
Local authorities say the snowfall was "unprecedented", and the avalanche risk in nearby areas has risen to the top of a five-point scale.
Trump - who made his name in politics by bashing elites, vowing to fight for the "forgotten people" and ignoring policy specifics - laughed and doled out compliments about his guests' entrepreneurial prowess. "I am sure about that!"
With several feet of snow on the ground, and sidewalks only partially shoveled, organizers have resorted to handing out plastic spikes that bolt onto shoes.
"The interesting thing is that if you have a prime minister who understands the fundamentals of economics, he does the right reforms and Modi is doing that", said Frank Appel, CEO of Deutsche Post DHL.
Trump's decision a year ago to recognize Jerusalem as Israel's capital roiled Arab nations and led Palestinians to refuse to meet with Vice President Mike Pence during his visit to the Mideast this week.
The tension is palpable.
The media was abuzz when the White House confirmed his attendance, waiting to see how Trump will use this global platform to promote his "America First" agenda, which is widely expected. How will the crowd react?
Trump says the two countries are now joined at the hip.
"They should listen to both sides", she said. "But maybe politics should change".
Earlier in Geneva, protesters laid a wreath at the entrance of the USA diplomatic mission in memory of Heather Heyer, who was killed in Charlottesville, Virginia, amid clashes between white nationalists and counter-protesters last August.
Rani said he was anxious that Trump would cast a shadow over the meeting.
The annual gathering at Davos attracts free-trade-loving political and business elites, who might be surprised that the protectionist-leaning American president will be in their midst.
The Trump administration has repeatedly lashed out at allegedly unfair trade agreements and practices, slapping additional import duties on products from across the world, claiming they benefited from unfair state subsidies.
"We certainly should feel encouraged, but we should not feel satisfied", International Monetary Fund (IMF) chief Christine Lagarde said on Monday in presenting an upbeat update to the organisation's forecasts for global growth, she attributed that growth to "cycles" but it is clearly the Trump effect.
Numerous other attendees, meanwhile, will nearly certainly jump at the opportunity to lay into Trump.