This is outside my area of expertise, but I think the equivalent functionality outside of ADO would be to retrieve the dataset into an array, then use standard array navigation techniques, rather than functionality that is specific to the database API.
If you're dealing with datasets that are large enough that you don't want to load the whole thing at one time, you should try to find a way to narrow the result set in the query before you start navigating the results. For instance, if you find yourself loading a result set, then just going to the last row, it's easy enough to make the query just return the last row in the first place. If you find yourself retrieving a result set, then looping through it (or filtering) for a specific row (or set of rows), I think you'll find that letting Oracle do that for you will show significantly better performance.
The reason that you need to use arrays to do this kind of navigation with Oracle is that Oracle cursors are always forward-only (whereas with ADO, you have dynamic, keyset, and static cursors as well). If you really need to be able to navigate an entire large result set, loading the whole thing into an array is about your only choice.