[RPG] Is a lightfoot halfling obscured for the purposes of hiding while in the space of another creature

Technically no. Fifth Edition D&D does not have a concept of facing. So creatures are assumed to be able to see in all directions freely. This would include directly under themselves.

The rules do not allow for creatures to block line of sight, so a creature certainly can't block its own line of sight with its own body. So as far as being obscured by the ogre, that's not possible in RAW 5E.

That said, if I was DMing this game, I'd allow it.

A note about sharing spaces and the justification of facing as an issue here (from comments.)

While the halfling probably can't share the space with the Ogre, the rules do allow the character to break up their movement. Does that mean you can attack/hide in the middle of a movement through the Ogre's space? Could you jump and fire over a short wall? I don't think these are adequately addressed in the rules.

The reason facing matters is that you can't hide from a creature when you are in plain sight of that creature. If you can't be behind a creature, what in the rules says you can be under them and therefore out of view?

By rules as written, you can only grapple creatures one size larger than yourself (PHB p. 195), so a medium creature can jump on a large and a small onto a medium.

Note that the second paragraph is an alternative, not a variant, so it too is in play. If the creature is larger than you can grapple and is suitably large, whatever the DM decides that is, you can simply use your movement to walk or climb it. The DM would need to decide which and if the creature was difficult terrain or not and if any checks are needed; presumably Dexterity (Acrobatics). Assuming the creature didn't want you there it could try to throw/pull/buck you off, resolve this as an opposed check.

Personally, I think it would be awesome if the players jumped and climbed up the dragon to try and sever its spine. They would too; right up to the point where I say "The dragon drops prone and rolls over you. Time for some saving throws."