Can 'pięknego' only be beautiful and not any of the similar adjectives like pretty or lovely?
no. you need accusative after "widzę", and accusative form of "piękny koń" is "pięknego konia"
(Horse is masculine animated , accusative=genitive)
i wrote a nice horse. i thing that it could be right too .What do you thing?
Not really. First of all, "nice" has a lot of meanings (and it could mean that the horse is nice to you), and if we were to interpret it in terms of beauty, it doesn't seem strong enough to me. I would treat "a nice horse" as "ładny koń".
lovely gorgeous or beautiful mean almost exactly the same thing in this sentence and should all be correct