Regarding Hybrids: I consider creatures such as Manticores and Chimeras NOT to be hybrids themselves; they are species with defined characteristics in-universe. Similarly with griffins/griffons and the draconequus/draconequi (e.g. Discord).
A Hybrid, to me, is an "unnatural" or "unusual" offspring of two well-defined species. E.g. A Changeling-Pony crossbreed.
*Since mules and hinnies are horse-donkey cross breeds, yes they are Hybrids.

And additionally in the biological definition: They cannot procreate, and griffins, Manticores and Chimeras can procreate in the Ponyverse.
Welp, I don't know about mules and hinnies, but I just go ahead and think that it is logical and they cannot.

3916896 Er...
Thank you for that interesting IRL biological tidbit.
Whether the hybrids' offspring can procreate or not was never an issue for me; I only wanted to go give some guidelines for submission to the Hybrids folder.
Now, if you want to discuss taxonomy and biology in the forum, please feel free.

Although the correct word is mutation, in my stories there are ponies who carry multiple traits from a ross the three species. The main mutation is winged unicorns who have a mixture of traits from the two species, such as the wings and horns,(although their genetics favor the unicorns) but they also have some conflicting traits that make their lives difficult. One in particular winged unicorn has the ability to stand on clouds, but at the same time bis bones are too heavy to make flight as accessable as it should be. Likewise, his wings have less feathers than normal and be does not have the underlying layer of feathers beneath his fur that seperates warm and cold air, meaning that higher altitudes would be too cold for him. On the opposite spectrum there are horned pegasi who are the opposite, with traits that favor flight than their horns.

Also to mention, speculation has come about that there are further mutations with earth ponies, such as Shining armor being incredibly big for a unicorn, but that field is less interesting because of the normalcy of the traits:

3918844

Um...
I'd say just as well submit such a story to the Hybrids folder; stories in the Other folder are mainly for sorting and/or holding, and I'm not going to kick your story (if you submit it) because you have mutations instead of crossbreeds.