Some suggested she felt humiliated following the release of naked pictures of Prince Harry partying with other women in Sin City.
Wednesday's ski-slope hug followed a more private display of affection at an up-market restaurant in the Swiss ski resort of Verbier.
"Cressida climbed on to Harry's knee," a fellow diner told The Sun.
"He started softly rubbing her hair then they began kissing.
"It was quite passionate - much more than a peck on the lips."
Prince Harry returned to Britain in late January after a 20-week deployment in Afghanistan in which he acknowledged he'd targeted Taleban fighters from the cockpit of his Apache attack helicopter.