the sentence means exacly what it means -You are touching a white horse. no hidden meaning behind it. you is one person.
It's hard to imagine a situation where this sentence works. Maybe telling a blind person what they are touching? Or describing a photo? Describing how to do something in smartphone with a white horse icon?
„Dotykać” is a verb with a few different meanings, some of which are separated by the case which the verbs connects to:
- Dotykam (kogo? czego? genitive) jej – I make psychical contact touching her
- Dotykam (kogo? co? accusative) ją – I'm being unpleasant to her; I upset her
Because here you are making psychical contact with the white horse, the horse stands in genitive.
funny it means to be unpleaseant to her as well, because the aquivalent word for to touch in german or also in english actually means to awake emphaty or to bring someone's emotion to the surface.
So the use of the case gets decided by which meaning of the word you want ? I thought it is always accusative, but in this case for animated males Akk- Sg= gen. Sg.