If you mean walking towards the mountain, we could say "Idę w stronę góry or Idę w kierunku góry. "Idę na górę" could be translated as climbing a mountain. But if you mean climbing, it is better to say "wchodzę na górę" or "wspinam się (na górę)" . If you mean hiking in the mountains we could say "Idę w góry" or "Idę pospacerować po górach".
I'd rather say "Idę do góry" in such a situation. Of course if I am going by foot.
"Idę na górę" is rather "I am going to another floor (above the one I am currently on)".
Uphill here could be translated as "pod górę" (meaning, the whole way is only up). So we can translate it as "Idę pod górę".
so why does the ó disappear sometimes when you conjugate the word and sometimes it doesn't?
Polish children are taught, when learning orthography (u vs ó, to be exact), that we write "ó" and not "u" jeśli wymienia się na "o" (if it 'changes' to 'o'). So this rule rather goes in another way that you ask, but it's probably the best I can find. Also not every ó does change to o, as you noticed. But I don't think there's any easy way to know which ones.
well isn't it that in general short one-syllable words lose the ó? mój, twój, stół, sól, móc...
I guess this thread is already too old, but the question is interesting. The short words you listed have the ó instead of o because the syllable there is closed, i.e. ends in a consonant. The /o/ in closed syllables historically first became long and then started being pronounced like /u/, but it's still written "ó" because there used to be an /o/ sound in its place. As soon as the syllable becomes open, like in "moja, twoja, stołu", it changes back to o, because the /o/ sound never became long in open syllables. But in góra, the syllable is open and seems to have always been so, and although I've tried looking for the reason o changed to ó there, I couldn't find any useful information about that. If anyone here knows the answer, please reply.