Conditions on the lower part of the Silvano Beltrametti piste delayed both races several times from their respective original start times of 9:30am local time (8:30 GMT) and 11am (12pm GMT).
World champion Svindal, who retained his 58-point lead in the standings over last year's winner Klaus Kroell of Austria, was left with mixed feelings about the cancellation of the men's downhill.
While it gave him his first globe in the sport's blue riband event, Svindal's chances of taking the overall World Cup crown are in jeopardy.
With only three races left in the season, including the slalom in which he does not take part, the Norwegian trails Austria's Marcel Hirscher by 149 points, a gap last year's overall champion seems almost certain to retain in the giant slalom and slalom.
"I have mixed feelings about today," Svindal said. "I'm of course happy to have clinched my first downhill globe but also sorry to have lost a great chance to score big points in the overall title.
"Marcel Hirscher fully deserves his second big cup, he has achieved an amazing season. I am also very pleased with my own winter, I have done a lot with my downhill gold medal in Schladming and my two crystal globes in the speed events. I hope now that the Super-G race will take place tomorrow.
"The jury took the right decision as the racing conditions were really bad with that fog," he added.
"I would have enjoyed racing the downhill course again today, I like it a lot but that's life."
There are rumours that he will strap on some slalom skis as a result, but he is unlikely to be successful in that discipline.
The subsequent cancellation of the ladies race meant that Vonn claimed the downhill title despite currently recovering from a broken leg in rehab in Florida.
"Omg I won the World Cup Downhill title!!!!! 6 in a row with a bum knee! Everything in life comes back around," Vonn wrote on her Twitter profile.
In 2011, the American, a four-times overall World Cup champion, lost the big globe by three points after two races were cancelled at the finals, also in Lenzerheide.
It was a 17th World Cup title for Vonn beating Austrian Anne-Marie Moser Proell's total of 16. Only Sweden's Ingemar Stenmark has more with 19 in the men's ranks.
Vonn beats Slovenia's Tina Maze, the overall champion, by one point in those standings. The fog ruined Maze's hopes of bagging all five crystal globes.
Slovenian Maze secured the overall title last month and could still take the three other disciplines.
Her current overall total of 2,254 points is a World Cup record after she bettered Hermann Maier's mark of 2,000.
A men's and a women's Super-G are scheduled on the same course on Thursday.
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- Marcel Hirscher