I didn't notice a difference in the number of nicks I get. There's definitely less irritation though. The whole reason I switched to straights was to eliminate irritation, so to that end I shave with cold water. It is pretty refreshing on a hot summer day, when it's 105 with 90% humidity that makes it feel like 115. Those days a cold shower and shave are glorious.
The only downside is when it gets cold outside. Right now in the middle of winter the last thing I want to do in the morning is splash cold water on my face. I still use cold water but I'm more prone to skip a day or wait until evening to shave.