I have never met a player who wants to play Ice King and absolutely refuses to take Magic Missile because it is force damage or Wall of Stone or Chain Lightning or other D&D spell icons, but if you want to restrict yourself that way, have at it.
One of the players in a friends AD&D campaigns would only research fire spells, to the point that the other PCs actually went on a quest specifically to get him Cone of Cold so he wouldn't suck so much.
After receiving it, he worked with the GM to copy it into his Spellbook as 'Cone of Fire'.