I agree with you. I also believe he is the Moon God or the guardian that represents the moon. I actually made a rather detailed post about FD and Majora. The latter sections focus on Fierce Deity:
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I've always thought of Majora being a demi god of sorts. Around Termina you have multiple symbols of which show the face of Majora - a big example being the Stone Tower Temple. This odd dungeon, when you entered, had what seems to be a section of Majora's face. As you can see from the picture to the right, it does bear some resemblance to the actual mask: you have the spikes (maybe horns) and you have the two eyes - with one being a switch.
Why exactly is the Stone Tower Temple a place of worship for Majora? We tend to associate Majora with all things dark -- the Stone Tower Temple is more so a light related dungeon. I think it's safe to assume this as within this dungeon your primary weapon is sunlight; Link uses his Mirror Shield to reflect sunlight and then goes on to utilise the famous Light Arrows. However, this seems contradictory, why would a place associated with sunlight worship something that dwelled within a moon? Majora, or the incarnation of it which is trapped within the mask, seems to reside within the moon. This baffled me whenever I tried to come up with an explanation on this theory, so I analysed the moon instead.
The moon is one of the main vocal points in the game and is a constant threat; however what if the moon isn't exactly evil? The moon was never meant to crash down, thus the impending doom was conjured up by non other than Majora. Majora controlled the moon, or in other words, hijacked it. The evil mask manipulated the moon so that it would crash down and destroy Termina for reasons we do not know (I'll speculate on this further down). Anyway I don't associate the moon with Majora nor do I associate it with evil. So what dwells within the inner chambers of the moon? Well it seems like a peaceful meadow and a tree that seems to bear much resemblance to the tree of life. Why would something so peaceful and serene be so destructive? Anyway, what am I getting at? Well if you look at the moon closely you can see that it's facd doesn't really look evil; it actually looks somewhat scared. It's facial expression seems similar to when someone "eeks", to phrase it. Now I looked into this further and does anyone remember the first day? You do a number of task and one of them is collecting the moon's
tear. This made me think, maybe the moon is showing us that it doesn't want to crash down and destroy the land; it shows its displeasure and empathy by shedding a tear.
This is why I think all of this started, I think Majora wanted to destroy Termina not for the sake of destroying it, but instead to obliterate the moon. But why though? Well I would like to reference the Stone Tower Temple again--like I said previously--it's a light theme, well more so sunlight. I believe that this Temple worships the sun, but it also shows symbols of Majora - thus why I believe Majora is related to the sun and is in fact the sun god. I was thinking more about the concept of light (sunlight) and Majora as well. If you look at the colours of the mask, even inside the boss stage, it shows multiple colours; it's almost rainbow-like. The colours are actually related to the
Visible Spectrum. These are colours that we can see with the naked eye due to a little thing called "sunlight".
So with Majora being ths sun god, or goddess, what about Fierce Diety? Well I believe these masks are the antithesis of one another. We already know that FD is a god of sorts as it's in the name: Deity refers to a god or goddess. I believe FD is the moon god and thus the antithesis of Majora. If we relate this to the colour scheme, FD has a lot of bland colours: whites, greys, blacks. Black is the absence of all colour and white being the existence of all colours. Funnily enough, the moon is white an black. When it's not in sunlight it is absent from colour (black); however the reason we can see the moon is due to sunlight reflecting off the moon and back down to earth (white). To further prove FD's connection with the moon just take a look at his armour: you can clearly see the marl of a triangle and a crescent, which in mythology, represents a moon. (It's located on his chest plate, click the
link for a clearer view).