The only notable Sonic I've played in tournament was Wes, back at Viridian 5. I lost, but that's due more to my lack of skill/match-up experience (at the time). Based on what I saw, he tried pretty hard not to get grabbed, and for the most part pulled it off (I did grab him twice, but messed both up early). Near the end of the second match, however, I started catching on to his playstyle and was able to stop some of his approaches with some pretty simple moves (it was too little too late, but you get the idea).
Sonic may be hard to grab, he has a bunch of moves that are safe on block (these tend to involve him getting behind the Climbers after the hitbox ends), and he has some tools with which to separate and gimp Nana. But at the same time his moves aren't nearly as destructive as the ICs'. They're such low priority that even something as simple as jabs can knock him out of approaches (this is what I started doing in that second match above). Even if he runs away, the ICs have desynch combos for flat stages (keep in mind that his aerial movement speed isn't nearly the fastest) and Up-airs for platform assaults (though I hear Sonics don't like platforms), and in general they have more potential for damage-dealing than Sonic does, provided you remain wise about what he's trying to do. Sonic is a mid-weight (0.985 times Mario's weight), so CGing is only slightly faster than the standard for Mario. CGing would also be the best way to get your kills, as Sonic does not die off the side as easily as you think (mid-weight plus great recovery). Overall, I'd say the match-up is in the Ice Climbers' favor, though not by a whole lot - Sonic has enough ways to effectively fight them that he can still stand a chance. No more than 60:40 in my opinion.