No a cold crash won't kill the yeast, it will cause it all to fall out of suspension, and then when I rack it off for bottling it won't be in the beer. I need to add another yeast, and I'm using Nottingham because it forms a nice solid layer at the bottom of the bottle, which allows me to pour a super clear pint. 1214 does not! It's easily disturbed even after ages in the bottle. Tastes great though. I fully intend to harvest the 1214 from the fermenter for the next lot.
Last time I cold crashed this beer I bottled, assuming the yeast would still be in suspension, and it didn't carb up. I went to the harvested yeast and added a small bit of sludge to each bottle and problem solved. But cloudy beer because the yeast is so easily disturbed. So Notty this time!