By Maggie Coughlan
December 09, 2012 11:00 AM
Chris Jackson/Getty

If you don’t think laughter is the best medicine, just ask Prince William.

Despite a stressful week – which included a pregnancy announcement, hospital visits and more – the dad-to-be has managed to maintain his sense of humor.

The Prince, making his first public appearance since wife Kate was released from King Edward VII hospital following a four-day stay with hyperemesis gravidarum (severe morning sickness), attended the Winter Whites Gala in London on Saturday.

Michael O’Higgins, a former chairman of homeless charity Centrepoint, which the gala benefited, told reporters: “[William] said they shouldn’t call it morning sickness, as it’s a day and all-night sickness.”

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Inside the event, William shared his more serious perspective on his country’s homeless population.

“About this time a few years ago, for one night, I gave up the warmth and comfort of my bed and tried sleeping on the streets of London. Of course, this was just one night. I was cold but safe and I knew I had a home waiting for me,” he said.

“Many others have no such luck. The cold streets are the only reality they know. And yet so often their spirit shines through. What these unfortunate men, women and young people could achieve given the right opportunities is limitless. I really, really believe that,” he continued.

William was originally scheduled to attend the British Military Tournament at Earl’s Court in London on Sunday, but has canceled and will be spending the day “privately with the Duchess instead,” a spokesman for the couple, both 30, said in a statement to PEOPLE.

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“It is well known that hyperemesis gravidarum often recurs and, until further notice, to allow the Duchess a degree of privacy during her pregnancy, we do not intend to offer regular condition checks or advise of routine developments associated with it,” the spokesman added.

The couple’s next engagement is Wednesday December 12, when they are set to attend the royal premiere of The Hobbit movie in London’s West End, but will decide as the date nears.

• Reporting by SIMON PERRY