The coldest MLB game ever was apparently played on April 23 of 2013: the Rockies against the Braves, and a 23F temperature in Denver at the start of the game. Quoting from this post by meteorologist Cliff Mass:
“Denver was an expansion team that played its first season in 1993. Thus, considering its unique meteorological location and altitude, it is quite possible that the 23F would have been the coldest temperature on record for all major league games at any location. Yes, you might argue about Minnesota, but keep in mind that the baseball season usually starts around April 1, and the all-time record low daily maximum temperature in Minneapolis for April was 22F in 1896.”
The Phillies-Rockies NLDS game 3 in Denver in 2009 apparently got into the mid-20s by the end of that game, with a wind as well. When you look at attendance for World Series games in the deadball years, you see quite a few times that cold and/or wet conditions kept the number of fans well below 10,000.
Finally: another meteorologist says MLB would drastically reduce the chances of games played in cold/snowy conditions if it just avoided home games in Minneapolis, Detroit, Chicago, Cleveland, Pittsburgh or Boston during the first 10 days of April.