I ran out of inspiration for the ultimate. I also considered "Colorless creatures you control "get +3/+3 and have flying and hexproof," but that excited me even less. Honestly I don't know that much about Ugin.

Funny how the morph thing works. "As Ugin is turned face-up, put three loyalty counters on it." should be cleaner, but planeswalkers always have this space issue when using offbeat abilities. I guess if you really wanted to you could always make a rule that planeswalkers are put as many loyalty counters as their printed card says as they are turned face-up. It wouldn't be immediately obvious, but people would agree that the card wouldn't make sense otherwise. Worth a shot maybe.

The first two abilities are amazing design, although I agree that the ultimate is less inspired. We don't know a lot about Ugin anyway, but playing up its affinity for colorlessness is a great idea.

But I would change some numbers. I'd be tempted to change the first ability to +2 (compare to Nissa, Worldwaker), but even if just chump blocking with lands, it's dangerous that it goes up so quickly while defending itself, so +1 is fine. The second ability, however, though a bit meh if you just try to use face-down things, is pretty bonkers when playing with artifacts, especially if Ugin is not immediately threatened or you can defend it at least for a short time. I feel it needs to be a -1. Depending on what the ultimate is, it could be just -6. It's not that good if people never get to it (as with Nissa Revane). Finally, I would try to lower the morph cost, but maybe just to since getting a discount for a planeswalker that your opponent didn't know you had / can't threaten when you want to use it is very powerful.

I made the morph cost as high add it is because he can gain 4 loyalty in one turn by turning himself face down and then morphing face-up. I did consider letting the morph cost, but only testing could say which option is better. The card draw ability should cost loyalty, you're right.
The current ultimate is neat, I think, and very powerful. I just don't know that it really fits Ugin.

This is a completely legal sequence of events:
"Bolt your face down guy."
"Surprise! Illegal target."
"Now that it's face up, Bolt Ugin."
"Bleh, it dies."

Hah. Assuming the first speaker has two different Lightning Bolts, yes. One of the casualties of the hacky planeswalker-damage rule.

The use of the first ability as a +4 is weird and cool. I think. I don't know if it might confuse people that he can't do it multiple times in a turn.

The second ability is awesome in any artifact-themed deck. Terrifying in a Kozilek EDH deck, but plenty good enough in a Kurkesh or Daretti deck.

I don't understand. How is turning it face-up and using its first ability so that it ends up with 4 loyalty different than just casting it normally and using the first ability so that it ends up with 4 loyalty?

That's not the clever bit. The clever bit is next turn, using the +1 on itself, then using morph to turn it face-up again and put three more counters on it.

You can also be super clever by using Ugin's +1 on himself, then leaving him as a creature for your opponent's combat phase so that he can't be attacked.

Oh, wow. Yes, that's something that definitely should not happen for all sorts of reasons.