I've been getting a lot of questions about this topic lately, so I thought I should highlight it again. Most people cannot use cold process soap as a shampoo. Shampoos are generally at pH 6.0 or lower, whereas soaps are alkaline, over pH 8.0. This means CP soaps are not pH balanced for our hair. After shampooing with products out of the right pH range, the cuticle of our hair doesn't lie down, and this can lead to abrasion between the hairs. This is a serious cause of mechanical hair damage, and once you have damage, it's hard to repair it, even with the most intense conditioners.
As a note, you cannot get a soap to pH 6 because it'll stop being soap!
CP soaps aren't as soluble in hard water as most surfactants. Soap molecules in hard water are converted by double decomposition to form insoluble non-foaming salts like lime, calcium, or magnesium salts of fatty acids. This isn't a big deal on your skin, but it can lead to build up on your hair, leaving it looking dull and feeling kinda crunchy. They won't foam well if there are metal ions in your water - and most water contains metal ions - and they won't foam well in the presence of sebum. Given these properties, CP soap isn't going to remove all the stuff you've put on your hair and you won't get a feeling of being clean (or, ironically, your hair might feel too squeaky clean, which isn't a good thing).
What I make as a shampoo bar is what is called a syndet or synthetic detergent bar, using surfactants. If you're interested in learning more, click the links!