A few photos from history:
President Dwight D. Eisenhower:

Two Countries, One Umbrella – President Dwight D. Eisenhower with Indian President Rajendra Prasad, in India, December 11, 1959 (anyone have the year?)
President John F. Kennedy
President Lyndon B. Johnson

President Lyndon B. Johnson arrives for church services in Honolulu, February 6, 1966, during Vietnam negotiations. To Johnson’s immediate right, Rep. Spark Matsunaga; on Johnson’s left, a Secret Service agent. National Archives photo
President Richard M. Nixon

Caption from The AtlanticWire: In 1960, Richard Nixon pledged to campaign in all 50 states. He was not even rewarded for this foolishness with nice weather in Hawaii.
My memory is that no other presidential candidate has campaigned in Hawaii since then. Has any other candidate campaigned in Alaska?

Collection: NASA Great Images in Nasa Collection Title: Nixon and Paine at Apollo 12 Launch Full Description: Dr. Thomas Paine, NASA Administrator, shields First Lady, Mrs. Richard M. Nixon, from rain while the President and daughter Tricia, foreground, watch Apollo 12 prelaunch activities at the Kennedy Space Center viewing area. Following the successful liftoff, the President congratulated the launch crew from within the control center. Date: 11/14/1969 NASA photo, on Flickr
The image of Nixon in the rain was captured several times.

From the AtlanticWire: Even amid his staff and security, Nixon looks like a lonely man helpless against the elements. (AP photo?)
President Gerald R. Ford

Wally McNamee photo, University of Texas Center for American History. UPI caption for their photos: As Betty Ford holds the umbrella, a military aide rushes forward to assist President Ford as he trips and falls on the lower steps of the plane ramp following his arrival in Salzburg, Austria on June 1, 1975. (UPI Photo/Files)
President Ronald Reagan:

Undated photo of First Lady Nancy and President Ronald Reagan being sheltered on an airport in an unnamed place. Image from BigotBasher.
Reagan at the White House, in the rain:
President George H. W. Bush:

Barbara Bush held the umbrella for President George H. W. Bush in July 1989 (in Italy?). From The AtlanticWire.
President Barack Obama:

President Barack Obama took the stage amidst a downpour at Abraham Lincoln National Cemetery in Elwood, Illinois, on Memorial Day. He announced that the event was being canceled because of the severe weather, and he told the crowd to seek shelter, May 31, 2010. (Official White House Photo by Pete Souza)
More:
- Obama scandals: Now, umbrella-gate (tv.msnbc.com)
- Sometimes an Umbrella Is Just an Umbrella (balloon-juice.com)
- Under My Umbrella: POTUS Edition (itsspencerbrown.com)
- Presidents Look Like Doofuses in Rain (theatlanticwire.com)
- From the 2012 campaign: “30 pictures of President Obama’s rain-soaked speech,” (buzzfeed.com) (Warning: Cute kids loving on Obama in the mix)
- Journalists, especially those with a rightward tilt, complain about the sunshine, moments before the rain (buzzfeed.com)
- “Presidents don’t use rain delays,” Brooklyn Public Library account of FDR’s 1944 campaign visit to New York and Ebbetts Field in the rain
- “Even Obama’s umbrellas are a scandal now,” Post Politics blog