Is a lightfoot halfling obscured for the purposes of hiding while in the space of another creature?

Only if lightly obscured

Lightfoot Halflings have the racial trait Naturally Stealthy, whose description states (PHB, 28):

You can attempt to hide even when you are obscured only by a creature that is at least one size larger than you.

This does not make any reference to being in another creature's space.

If the character is lightly obscured by a creature one size larger than them (generally size Medium or larger), then Naturally Stealthy allows them to attempt to hide. Otherwise, they must meet the regular standards for hiding - namely, DM say-so and not being clearly visible.

There is nothing to suggest that being in another creature's space affects a halfling's ability to hide.

You can't willingly end your move in another creature's space

While there are ways to unwillingly do this, there is no method within the rules to willingly end your turn in another creature's space. From the "Moving Around Other Creatures" section of the rules (PH p. 191 / Basic Rules p. 74):

Whether a creature is a friend or an enemy, you can’t willingly end your move in its space.

But what if I end up there unwillingly?

At that point, it's up to the DM to determine if you can hide there. If you ended up there unwillingly, your movement was likely seen, so a DM may not allow a creature to suddenly have no idea where you would have gone.