Ridley's recovery can actually be deceptively tricky if you were to try challenging it. The three jumps give him a bit of extra leeway and while his up special only recovers from three directions it is actually quite difficult to challenge and is a powerful KO move, I've taken a fair share of KOs from people who thought they could contest my up special. His side special recovery is a command grab that can drag you to the abyss and that's especially bad since the Climbers rely on each other for recovery. There are characters who can have success exploiting Ridley's recovery, namely another Ridley, but I don't know if the Ice Climbers are really one of them.
Ridley is a character who likes to use disjoints to space the opponent, his plasma breath can force approaches, and a lot of his toolset is based around getting the opponent off stage and being able to keep them there. I think Ridley's biggest problems will come from is good enough recoveries to deny his edge-guarding, characters who can beat him at his own spacing game, or characters who can work their way in and turn him into combo food.
Now I'm not an expert on the Ice Climbers or what all of their best options are for given situations, but I think their biggest advantage is their potential to be combo heavy characters, and Ridley can get eaten alive by those once they get going. Keep an eye on what the player is doing as well, if you're able to bait and read his command grab that's your opening to start doing damage, and if you're having trouble getting in against a defensive Ridley then pestering with ice shots at mid-range could get you in close (I wouldn't try ice shot zoning from longer distances since you'll risk dealing with the rivers of fire he can send your way). Still have to be cautious up close and personal with Ridley because that FSmash kills incredibly early and DSmash can have a deceptively wide range. Just don't rush in too aggressive because that's playing to his advantages, be patient to find your openings.