So, in Ringfinger Leonhard's Silver Mask description, it says,
In his youth, Leonhard suffered grave burns to his entire body. His face in particular, which he hid beneath his mask, was terribly scalded.
Looking at the silver mask, it is a very simple frame with a tricorne on top.
Now look at the Mask of the Child.
In its description, it states:
This mask, belonging to the naive child, slightly raises stamina recovery speed.
The parallels between the silver mask and the Mask of the Child are that the mask belongs to a naive child, and Leonhard suffered injuries when he was in his youth. Although "his youth" could very well mean anywhere from an infant to late teens, it is still a possibility that Leonhard was this naive child.
Next, both masks are made out of the same silver-like material. Pinwheel is three individuals into one, and each wears their own respective mask. That means that in Dark Souls 1, Pinwheel would have had to take the mask of Leonhard or consume Leonhard, and create the mask's unique shape and image, as well as enchant it with the stamina regeneration.
My theory is that Leonhard was originally the child that was inside of Pinwheel, but an event occurred that broke the three of them apart. In VaatiVidya's video on Pinwheel he suggests that Pinwheel is working tirelessly to separate the three into individuals and not one combined unit. If left unattended, they would eventually succeed, and perhaps Leonhard was spawned from this, still wearing the child's mask that he put on after receiving his grave injuries. Over time, the mask would have become worn down, and he would have put the tricorne on top to cover the erosion of the mask.
However, the mask could have also been obtained by Leonhard in his late teens. He could have fought Pinwheel when invading a world in search for pale tongues, and come across Pinwheel; the fight giving Leonhard his injuries and obtaining the mask. He could have gradually worn it down over time, and put the tricorne on top to cover the impurities of where the "hair" was on the mask. However, this theory does not support the insert about the Mask of the Child's description and how Leonhard is the naive child being described, since he would be a young adult at this point, and even if worn down, the mask would most likely still be able to regenerate stamina in some form.
Another problem with the most recently mentioned theory is that in the last line of his mask, it says:
He abstained from restoring these injuries, even after becoming a Finger of Rosaria.
This implies that in Leonhard's life, he first became injured, donned the mask, and then joined the Fingers of Rosaria. Also, a flaw with these theories is that it specifically uses the word scald to describe his burns. Scald is only used in terms of water, implying that something water-based would have had to occur. Something like… a hydra?