Would cold water give me a better shave?

The most important part of a good wet shave, uming that the blade is already sharp enough, is to get the hairs as soft as possible. A dry shave is a really bad idea because the hair is still very tough and will often tear the skin before sucbing to the blade. The best way to soften the hair is prolonged hot soapy water. Thus in fact the best time to shave is at the end of a shower. This will give you a close, painless shave free from razor burn.