As Azure Sage noted, there is no one dominant religion in Hyrule but rumor has it that prior to the creation of the third game, Nintendo intended for Hyrule's religion so to speak to be modeled off Christianity. That said, the decision was ultimately dropped on the grounds of polarizing fans, some who would no doubt fear Nintendo was intermixing religion with fantasy. In the NES original, for example, the spell book used in tandem with the Magic Wand to emit fire was dubbed the "Bible" in the Japanese version. Another interesting similarity to note is the Trinity reference through the Triforce although that pertains more to a Japanese dynasty symbol which Miyamoto once observed and took inspiration from than a specific religion.
The closest we see to religion in Ocarina of Time specifically is through the spirits inhabiting several sacred objects. This is likely a reference to Shintoism, the native religion of Japan. In said belief, everything is deemed to possess a spirit of kami of its own. Prominent examples include the Great Deku Tree and Jabu-Jabu worshiped by the Kokiri and Zora, respectively. While to a Western gamer, these fail to qualify under the traditional notion of an omnipotent "deity", to the Japanese and other oriental players, these are very much so gods, the ones who govern the laws of nature.