I don't know about cold water passes - I've never done one. But I always do my against the grain pass with just warm water from the basin and no lather. I've never had a problem with lubrication doing this and I find that I can see what I'm doing a bit better without lather - a little line of black whisker dust precedes the edge.

But apart from that I can't say there's more to recommend it than re-lathering - just a personal preference on my part.

James.