Gore is a United Nations Foundation executive who also participated in the Summit on the Summit trek to raise awareness and funds for global water programs.
Gore said the expedition reached the mountain top Tuesday after six days of hiking.
"I walked over to Jessie and gave her a big hug," Gore told People.com via satellite phone. "The two of us embraced and we just cried. Every single one of us was in absolute tears. The temperature was zero degrees and so many people were struggling ... . People had hurt limbs, people had altitude sickness."
Gore went on to say the hardest part of the trek was the end when the group was faced with "a complete whiteout."
"There was so much snow, we could only see two or three feet in front of us. So we had to line up like a chain to make it to the final point. I'm so proud that every single one of us 12 climbers made it," she said, adding they headed back down almost immediately and reached the base of the mountain Wednesday night.