Against what? 
Ice/Cold is pretty impressive but you will learn what ATs/powersets to avoid ...
Synaesthetix:if your mum wasn't already dead I would go kill her for bringing
you into the world
My Ice/Dark has taken on a good number of Blasters in the zones one-on-one (or on one memorable occasssion, two-on-one 
) and won. She can also stand up to a lot of Scrappers for a good while, but would always run out of endurance before being able to finish them off.
I've never really gone in for actual duels, mind you - this is just from hanging around in the zones and running into someone when no one else is nearby, and so on.
Ice is HELL in PVP to scrappers. Because nothing irks a scrapper more than not being able to move. Even when we get ranged attacks, we love punching/kicking/smashing things, and ice corrupters are great for stopping that goal.
An ice/rad corrupter is hell on earth due to the slows and huge debuffs, and I've gone one on one with a few, and never won. Ice/cold could work to, but I've not seen many colds in PVP.
Oh, and get fly. Sure, it's not actually great and takes 2 powers, but if you want to make a quick getaway then flying vertically is hard to beat.
Ice/cold is very VERY good in PvP, insanely good. Pick up your 3ice blasts,freeze ray, aim, single target debuffs, aid self and acrobatics and your good to go.
/Kin is great if slotted properly. You can drain people in an instant, which makes Tanks/Scrappers/Brutes a doddle. Your massive Damage switchers can definetley turn the tide as well. Stack on a few Siphon Speeds, and they're pretty much stuck.
My main PvP toon is an ice/ice Corruptor and I can say without doubt that it is a VERY good solo PvP killer compared to other Corruptors.
You do have the squishiness most Corruptors have and and the lack of a heal can make it a bit less self sustaining than something like a thermal but that's a small price to pay.
Attacks wise, you're looking at the first two in the set and bitter ice blast as your only real damage output. Infrigidate, benumb, heat loss, snow storm... You're going to be spamming all these to bring targets to a halt before going in for the kill.
Freeze ray is also going to be your best friend and will account for a lot of kills for you. Slot it for rechage so it's up as much as possible and spamming it will help break mez protections on squishies.
Beware of SR scrappers as their resistance to slows will be a particular danger and spine scrappers will also be a pain because of the range. However, any other type of regen scrapper will hate you. Your slows will enable you to stay out of range, taking potshots at them while crippling their self heals. Still quite hard to put them away as end will normally run out before you can but you'll annoy them and unless they get the drop on you, aren't a threat.
Trollers are also a threat due to the lack of mez protection so try to hold them with freeze ray or end drain them with Heat Loss ASAP. Other than that, you can hold your own quite well as long as you know when to run.
Is any Corr viable for PVP solo? Yes,some of them ice*fire/cold*rad*kin ....as long as your enemies solo too(wich ...is not gonna happen) 
PVP in this game is not meant for soloing.You could do very well against isolated specific enemies but any team(and almost everybody teams) will crush you.
I am a Ice/Cold Corr, just L14 atm. I am prepping for PVP. Is any kind of Corr strong enough to hold their own in PVP?