So i have a question about this wonderful attack and its static text which says that "If your opponent has no momentum, this cards difficulty is 5, and it gets Powerufl:3".

My question is this: Say that i'm playing Guy (either incarnation), for example, and i make sure that my opponent has no momentum when i play this card at its now-5-Diff. During the Enhance phase, however, my opponent manages to generate momentum. Does Hozanto still have the Powerful ability since I played the card when they had no momentum, or is the Powerful ability now null and void?

It's a continuous ability so as soon as they gain momentum, the difficulty and Powerful ability will revert.

Of course if you play the powerful ability and THEN your opponent gets momentum, you keep the dmg bonus correct?

Yes, because at that point the damage bonus has already resolved.