Road teams do win quite a but, but it's usually a split. These are the times both road teams won in the Semifinals in the Super Bowl era:
2012
1997
1992
1966
Before the Super Bowl era there was usually only a single championship game, though they sometimes had a play-in game to break ties in a division race. This was true for the NFL, AFL, and AAFC.
2012, San Francisco beat Atlanta as a road favorite while Baltimore pulled off a major upset against New England.
1997, Green Bay and Denver were both road favorites.
1992, Dallas pulled off the upset in San Francisco while Buffalo was a road favorite at Miami.
1966, that was a long time ago and rules were different. Home field was decided on rotational basis as both road teams had superior records and would've likely been road favorites (or near pick-'em at worst).
2012, San Francisco beat Atlanta as a road favorite while Baltimore pulled off a major upset against New England.
1997, Green Bay and Denver were both road favorites.
1992, Dallas pulled off the upset in San Francisco while Buffalo was a road favorite at Miami.
1966, that was a long time ago and rules were different. Home field was decided on rotational basis as both road teams had superior records and would've likely been road favorites (or near pick-'em at worst).