Seems to me that either a 1-piece or a 3-piece airlock will allow air to come back in, just as easily as it lets air out. I don't understand what it is about either design that would make air travel one directional.
I cold crashed in my primary for years and just recently switched to cold crashing in my kegs as part of my current focus on reducing oxidation. I think most of my problem was that I wasn't adequately purging my kegs, but I also think cold crashing with an airlock isn't ideal for a couple reasons.
First, whenever I went to transfer my cold crashed beer from my primary to my keg, the liquid was still in my 3-piece airlock but there wasn't a vacuum inside my primary. The only explanation I could come up with is that air came in to fill up the space. Granted, I couldn't actually see that air was coming in, but I also couldn't see that the airlock was keeping air out. I'm just trying to reason this out.
Also, we know that oxygen dissolves more easily at colder temps than at warmer temps, which suggests any oxygen in the head space is more likely to be dissolved into the beer during the cold crash storage period and especially during transfer than with a beer that's at ferm temps.
I don't know if the amount of oxygen I was picking up during the cold crash and subsequent transfer is meaningful or not, but I do know that my oxydation problem is gone now (again, this probably has more to do with me being more fanatical about purging the keg). I also know that gelatin clears the beer just as effectively either way, so I'm not willing to take the added risk of crashing in the primary. Plus, cold crashing in my keg as opposed to my primary gets my beer on gas 24-48 hours sooner, which means it's in my glass 24-48 hours sooner! YMMV.