Note that both in the English original and in the proper German sentence, the second part is, in fact, a subordinate clause that is introduced by whether in English — and that can luckily be translated directly into ob in German. So we can use the following as a starting point:
Es hängt ab vom Wetter, ob …
However, abhängen, being a separable verb, would like to have its separable particle ab at the end of the corresponding sentence. So we reorder it to:
Es hängt vom Wetter ab, ob …
Now let’s take a look at the whether we will go skiing tomorrow or not part. Our conjunction is ob — we already established that. We is the subject, our main verb is to go skiing which is in future tense. And then we have the or not at the end that we’ll come to later. Remember that future tense is rather uncommon in German so you were correct in assuming present tense instead. However, we have a subordinate clause, so the verb should be last.
Es hängt vom Wetter ab, ob wir (subject) morgen (time) Ski fahren (finite verb).
And finally, we add the or not, translateable to oder nicht to the final construct. It can be seen as a shortened co-ordinated sentence (oder being a coordinating conjunction) and we can thus just put it at the end.
Es hängt vom Wetter ab, ob wir morgen Ski fahren oder nicht.