Could somebody get arrested for being drunk while riding on a bicycle?

Florida can charge you with operating a vehicle under influence though to be fair they don't ever.

I believe so. A cop could make the argument that you’re still a danger to yourself if not someone else.

And while riding a horse, too...

Yes

Yes

Could here, public intoxication.

Yes, I have seen people arrested for riding a bicycle drunk here in California. Might depend on the state though.

Yes, I believe in most places you can get arrested while drunk in public period. If you aren't acting in a normal and safe manner.

Probably not arrested. But I could see them in protective custody.

You could even get arrested for walking drunk.

Since it exacerbates the problems of being drunk and disorderly

I have actually seen it happen one time.