Connacht Rugby CEO Gerry Kelly said that all options were considered, including moving the game to an afternoon start on Saturday as well as looking at other venues.
"The Dragons were due to fly from Luton to Galway on Thursday but they told us they would have difficulty getting to the airport, especially following the overnight deterioration of the weather in the UK, and even then there would be no guarantee that flights would be operating," he said.
"Taking all factors into account and following discussions with the Dragons, which we have been having daily since the weekend, it was felt the best decision was to call off the game at this stage.
"We discussed the matter with the Magners League and the difficulty our supporters might have trying to get to the venue was also a factor."
The pitch at the Sportsground has been covered since last Thursday and since then heaters and another cover have been applied.
Like last weekend's postponed clash with Leinster, the Dragons game will be rescheduled and tickets purchased for Friday's game will be valid for the re-fixed tie.
"We want to apologise to supporters, especially as the Leinster game was also postponed, but the safety of everyone has to be the number one priority," added Kelly.