Actually the figures discipline was the toughest to do outdoors because there was often ruts in the ice and the snow had to be cleared.
As Barbara Ann Scott experienced during the Olympics (figure skating held outdoors) in 1947:
1947 was the year when Scott accomplished the unbelievable. She was the first North American to win the European title and the World Championships in the same year. But in 1948, Barbara Ann Scott was unstoppable. Not only did she successfully defend her European and World titles, she went on to win the Olympic gold medal in St. Moritz, Switzerland.
Scott won her gold medal on an outdoor rink, which was uneven and dented by the men's gold medal hockey game between Canada and the Czechs the night before, which Canada won.
Apparently the temperature was just above freezing, and someone had tried to flood the ice. By the time the sun rose, the ice was a slushy mess. But Scott was unruffled. "When you have to skate outside in the elements, you tend not to worry about the small stuff," she said at the time.