There is an exception. Magic Equipment cards (with broken gems) can only be used by Survivors that have reached the appropriate Danger Levels. All other cards should be usable by pretty much anyone, though.
But, so far, there are no spells or enchantments with level limits. Anyone can use spells.
It even has a fluff explanation in one of the character bios. Something about how there are complex spells that require real magical skill, but those spells aren't useful in an apocalypse scenario, due to taking too long. So the spells available are basically spells for noobs and hacks.