As I see it, Nunu suffers from a split identity issue. He relies on AP for his E and R to do damage, but if you invest in AP to be more than a slowing machine, you are way too squishy to survive a well executed Ult. If you focus on building tanky then all you are good for is slows (which is a pretty forgettable CC) and neutral monster control.
So...
Passive needs touched up. A spell without mana cost is nice, but pretty sad in comparison to others. I don't have a passive concept for the rest of this kit.
Q is mostly fine. It would be much better if it was usable against champs for lower damage than vs minions/monsters. It feels too narrow in use currently.
W is just godawful. On the face of it a move speed and attack speed buff for you and an ally sounds good, but in practice isn't great for an ally and faster noodle slaps from Nunu is just trash. Complete replacement is best.
My idea of a replacement...
Grapnel - Nunu throws out a grappling hook on a rope. If it connects to terrain, Nunu can reactivate this skill to have Willump grab the line and yank the duo to the hooks connection point. If Nunu throws the line to open ground, the hook can be grabbed by an ally and Willump will pull them together. (Basically Nautilus dredge line but works only to pull two allies together.)
If the grapple strikes an enemy champion, it deals 5 true damage per champ level (no scaling) and falls to that spot on the ground for half the duration it could be grabbed by an ally.
Grapnel passes through minions and neutral monsters.
E is mostly fine. It could be tweaked as a skillshot with a bit longer range and maybe a tiny AoE for a little more interaction, but is OK.
R could use some love. It's a fun skill, but if you don't have another group CC skill on your team it's very hard to get the most from it. So here's an idea to incorporate the idea of Nunu being a little mountaineer with a yeti pal.
R- Avalanche Duo - Nunu takes a flying leap from Willump's back, burying a pair of climbing axes into his landing spot. Willump grabs the ropes attached to these axes, leaps up, and after a short delay yanks himself to slam down in the same spot. These leaps can pass over walls, with the size of walls passable scale up with ranks. While separate for that brief period, both Nunu and Willump can be targeted by enemies and share the same HP. Defensive items if used, such as Zhonyas or Barrier would only affect Nunu.
Nunu's initial impact area is small, deals minor damage, and applies a short slow. Willump creates two diameters, his moderate sized impact AoE knocks up enemies and does major damage, while the broader blast of arctic air he creates around his landing spot does moderate damage and a minor slow.