Either you edit in more factions separated by comma into the skins.txt, like:
factions = hungary, germany, ussr
This makes the skin selectable for those three countries.
BTW, people who do scenarios can also script units to be skinned by trigger, then the faction limits are ignored. This gets improved with Red Storm, when this is out you can also unskin by trigger.
But it's also possible to make a skin available for all factions by simply leaving out the faction entry in skins.txt alltogether, like:
[WINTER_5]
id = 22
texture = winter_5
category = land
This skin works for any country, provided its units do accept skins. Which is a work in progress still, but the list is growing.