Actually this makes absolutely no sense. The good thing is that in no other situation will you say wspinać się 'pod' coś - mówimy na wzgórze, na pagórek, po schodach etc.

You can also say "On wspina się pod górę". I think that we use "pod górę" in polish, cause then we automatically know that it is a hard climbing;) Or that the road lead us uphill. You can also say "On wspina się na górę/On wchodzi na górę", but it's not grammatical, though we talk this way. If you say "On wchodzi na górę" it could mean that he comes to the first floor, for example he lives on this floor. You know, "góra" = floor, it's colloquial language:)