I think it would be fine if the character is done well, but I don't trust magic (or most forms of media) to do that. Most of the time they just come out...bad.

What does "horny" as a character trait mean? With rare exceptions, everyone experiences sexual desire. Defining a character as "horny" is no more useful than calling them "sad" or "angry." Perhaps it's more useful to break down the question by the ways in which a character can express their sexuality.

If you're thinking of a character that is lecherous or promiscuous, that's a personality trait common across media. Tropes like the dashing rogue or the femme fatale come to mind. There's nothing wrong with a character that flirts or flaunts their sexuality, or uses it as a means to get what they want.

If on the other hand, you mean what Apple mentioned -- a highly active sex drive -- that's not a personality trait. It's something that we can't know unless the character makes it obvious, i.e. by being lecherous or promiscuous in the first place, or if we're privy to their internal thoughts. This in and of itself isn't a bad thing either. The breathless protagonists of romance novels make them all the more enjoyable for their target audience.

The danger of a character defined by their sexuality is that they are objectified, and only defined by their sexuality. That's when they cease to be a character, and instead become a strawman or a shallow wish-fulfillment fantasy. From there, it's easy to cross the line into bad taste, because of the taboo nature of the subject matter.

Nevertheless, I believe that sexuality is an important part of character writing, and can be human and compelling when done well. It's not about whether or not the character is "horny." It's about what that means for the character, and how that plays into the larger themes of the story.

I think it's important to differentiate between two kinds of "sexual" characters: those who are considered "sexual" because of their sexual desire, and those who are considered "sexual" because of their sexual desirability, either by other characters or the audience. In the first case, their sexual desire is part of their character, and it's something experienced by them. In the second case, being sexy isn't a personality trait, and it's not experienced by them, it's experienced by whoever it is that sexually desires them, be it another character, or a member of the audience.

So, why should we care? Well, there's two sorts of problems that can arise from screwing this up.
1: If you think sexiness is a character trait, you can end up with a really shallow character. If you make a character whose sole defining characteristic is being sexually attractive, they won't be very interesting, even though they may draw interest from certain audiences.
2: Perspective. A character's sexual desires come from the perspective of that character. A character's sexual desirability comes from the perspective of other characters, or a segment of the audience. If you force the audience into one character's perspective, you can end up with them losing empathy for other characters. You can also end up with the audience projecting the perspective character's desires onto the attractive character, and assuming that their desire must be reciprocal, and that's just creepy. Or, some segment of your audience whose sexual desire doesn't align with the perspective you gave them might get sick of it and decide to drop your work.

The only examples I've experienced that come to mind are:
1) School Days, best summarized as "What would happen to a harem anime if the main character was a horny teenager?"
2) Scorpion Shards, where one of the character is consumed by a supernatural urge to have sex.

The first one having a lot more down-to-earth approach to it, albeit still a mostly negative portrayal.
I guess Yoshikage Kira from JoJo also fits the bill in a more fetishy way, but he's also an antagonist.

I'm actuallly experimenting with a Planeswalker OC (similar to a Jack Harkness-like character, where it's a part of their lifestyle, and played for laughs in context only when his sex drive is cranked up)

I wanted the character to be Red/White and have a Dack Fayden-style "lovable troublemaker" vibe. I could see a Red/Green character being driven sexually as "my goals include planting my seed wherever it may grow on whatever plane suits me", though I'd like an approachable character who MAY experience one-night-stands, or humorous "not sure how human-on-merfolk would transpire, but I'm up for anything" or to the most extreme, having a disconnected multiplanar harem of sorts, however overall still does it for more overall than just physical gratification, and he does hope that his experiences may lead him to forming a bond with another humanoid with whom he can feel committed to bringing his planeswalking days to an end.