There really is no world-wide cross country running circuit of repeatedly held competitions to build an audience and following. You have a few events in Europe, but none in the US, Asia, Africa, etc.
Yes there are many cross country running races in the USA at the high school and collegiate level, but these are not open competitions that anyone can enter.
There is nothing for cross country running like the Diamond League or World Cup events in skiing and other winter sports.
That lack of world-wide interest and elite level open competitions in cross country running will hurt its chances of being included in any summer or winter Olympics.
All current Winter Olympic sports depend on either ice or snow to occur. Part of the resistance to including XC running in the Winter Olympics is XC running events do not depend on ice or snow as an essential element of the competition. XC running is possible on ice or snow, but there are few XC running events regularly held on ice or snow.
If XC running somehow made it into the Winter Olympics it would not necessarily have to be on snow or at altitude. There have been many Winter Olympics where there are numerous other venues for various sports (sports that depend on ice such as speed skating, figure skating, hockey, curling luge etc.) at lower elevations and/or in places where there is not any (or as much) snow. These ice sliding venues are often located far from the snow sliding venues. For the ice sliding sports they create specific venues with human made ice.
It is unlikely that the Olympic level nordic ski courses would be used for an Olympic Cross Country running competition. FIS regulations specify that elite level nordic ski courses be challenging for nordic skiers, with a total climb of 250-420 meters over a 10km course. For the metrically challenged that is 820-1377 feet of climbing over a 6.2-mile route, with the same amount of descent.
That amount of climb and descent is far beyond any all known cross-country running courses (guessing the 10km course in Tallahassee had perhaps less than 80 meters of total climb, so imaging a cross country running course that was over three to eight times hillier than that).
Running cross country on nordic ski courses would be more similar to running trail and mountain races than running track and road races, and would likely not attract as many top track and road racing athletes.
Also, high quality groomed nordic ski tracks generally prohibit all foot travel to preserve the snow surface, and making an exception for a bunch of runners would be disliked.