With temperatures set to dip to minus 10 Celsius (14 Fahrenheit), the Swedish Football Association has already stated its desire to keep the elements at bay for the Group C clash.
Swedish team manager Lars Richt told Reuters that their primary concern was for the fans who do not want to watch a match in Stockholm's freezing temperatures.
Trapattoni, however, is keen to protect his players' eardrums at the expense of the shivering spectators at the newly-constructed Friends Arena.
"When it is closed, it has an echo, which is no good," the former Juventus, Inter Milan and Bayern Munich coach told reporters on Monday.
"It is too loud. I was in Germany with this situation before, and it was bad for us because of the crowd...
"It would not be cold. The pitch is what's important. It's for the spectators that it will be cold."
While local media have fanned the flames of the debate, Sweden midfielder Sebastian Larsson said the players were unlikely to be bothered either way.
"Honestly? I couldn't really care less about it. For the players on the pitch it's not going to make any difference," Larsson told Reuters.
The final say about the roof will rest with FIFA's match commissioner who will make a decision on the day of the game after taking representations from both teams.
Friday's match will be Sweden's first competitive international at their new arena, and they come into the encounter on a high.
They closed out 2012 in fine style, staging a remarkable comeback to draw 4-4 with Germany in Berlin and snatch a vital point.
They opened the new stadium with a thrilling 4-2 friendly win over Roy Hodgson's England, with captain Zlatan Ibrahimovic netting all four goals, each one more spectacular than the last.
The Irish, on the other hand, limped out of 2012 with a crushing 6-1 defeat by the Germans and a lucky 2-1 win at Kazakhstan thanks to very late goals from Robbie Keane and Kevin Doyle.
Those results left Sweden in second place on seven points, three behind group leaders and favorites Germany, with Ireland one point further back in third.
With the Irish due to face fourth-placed Austria in Dublin on Tuesday, Trapattoni will be aware that two defeats would probably end his side's hopes of qualifying for the 2014 finals in Brazil.
For Sweden coach Erik Hamren, the picture is much more positive - a win in Stockholm followed by victory away to Austria in June would put them in the driving seat for second spot and a playoff place.
The Swedes will look to tighten up a defence that conceded four against Germany and hope that Ibrahimovic continues his fine run of scoring form since joining Paris St Germain.
Ireland have not been helped by Trapattoni's controversial selection policy.
Despite winning a penalty and scoring the winner against Kazakhstan, the experienced Doyle is only on the standby list for the current squad.
Hamren described the match against England and the February friendly against Argentina as "a party for the people", but he is now looking forward to the first competitive game.
"Now it's the thrilling fight for points, and I'm very excited," he told Reuters.
Sweden: Andreas Isaksson; Mikael Lustig, Andreas Granqvist, Jonas Olsson, Behrang Safari; Sebastian Larsson, Kim Kallstrom, Rasmus Elm, Alexander Kacaniklic; Zlatan Ibrahimovic, Tobias Hysen
Ireland: David Forde; Seamus Coleman, John O'Shea, Ciaran Clark, Marc Wilson; Robbie Brady, Paul Green, Glenn Whelan, James McClean; Robbie Keane, Shane Long