Violetnred

As mentioned above, Skylords work by turning the dreams and wishes of mortals into the various cards the player uses. This both explains why the cards you use and the campaign versions are not identical (you get all of them second-hand and can't just create the real version) and why it's appropriate to use any deck you want for any mission.
 
If you were to attempt something like this though, it's important to note that outside of perhaps the two Nightmare maps and Passage to Darkness you wouldn't be able to use Shadow cards given they are typically evil.

and interesting throught. I agree there are some pointers on some missions for factions that fit thematically. like the first line of missions where Frost fits most, since you could argue the active Skylord is drawing from their dreams and visions. 

Part of the appeal/selling point of battleforge is the customisation options, so I dont think this was ever the case. You play as a skylord, who has the power to summon creatures of legends and dreams of mortals. In theory, you aid them as you, so even though you are helping humans of say, Frost, you are still you. 
If you want a bit more flavor, I suppose you could match your army with the mission at hand. 

Most of the first maps are very nature/frost like. I guess for all the maps taking place in the snow, you ''should'' stick with frost. 
The Renegade Campaign (basicly the maps on the bottom of the World map) are in Fire and Bandit Territory, so it makes sense to play Fire and Shadow there. 
So I guess on average: Twilight Campaign: Frost + Nature (focus on frost), Renegade campaign: Fire + Shadow (with a focus on Fire).

The 12 player maps have skylords ''from all lands'' defending the world, so I guess you can play whatever you want there.