Good Lord. The expense and logistics of this aren’t worth the effort. As it stands, the NHL only has one refrigeration truck for outdoor rinks (they may have two now).
At best you are doubling that expense off the top. Secondly, availability for the facilities - especially stadiums - is tied up months in advance. I doubt the league would want to stage a marquee event in an abandoned mall parking lot at the last minute. Especially when the rinks need at least a week to get built.
Thank God Gary shot down the concept already. A regular rotation of Olympics and World Cups is the White Whale to chase right now, not a gimmick tried by a different league that may not even exist in five years.
Like I said, it can be set in advance. If you end the group stage by late November, it gives them enough time to find a venue where it might be suitable for outdoor and sell tickets one month in advance. Sometimes people will change their plan at a last minute if it's once in a lifetime opportunity arise. If they set a predeterminate open date that must be filled in, that would be three dates between Christmas Day to New Year's Day. It can be December 22 or 23 for a QF game, giving them time to set up a semi-final outdoor rink on December 27 or 28th and the final on January 1st.
In-season tournament can be good if it's outdoor spectacle. If it's indoor all the way through, it is same as a regular season game that is not worth our time having in-season tournament all indoor but if you add outdoor element to it, it can be huge and everyone will want to participate in that and every player would be up for it since it's outdoor tournament. You start the group stage indoor and players will go hard for an chance to play outdoor, final 8.
Now, if you said that they may have two refrigeration trucks, they can always buy more and is worth the investment long-term. Once a QF is done, the availability of truck may free up and can set it up at another city (third seed) that would take a few days to set it up and may not be used at all if there is no upset but if there is an upset in tournament bracket, it is all ready to go and sell tickets. It could easily be sold out if there is a final. 4th seed in a SF has no chance of hosting at the championship game anyways.
Most cities have football or baseball venues and even in college football stadium on campus that is not in use as it's end of the season and the NHL might do diligence inquire them of the hosting possibilities without any setback beforehand without guarantee and commitment after NFL release their schedule There will be no issue in Canada since CFL season is over at that date.
Gary may shot down this concept but has he thought of outdoor element to in-season tournament. I'm sure he will jump to this opportunity. If it's all indoor in-season tournament, he has the right to shoot it down. I know I would shoot it down.