CP soaps tend to be smoother than HP soaps. Not all scents will hold up in CP as they will in HP.
With CP, you are letting the natural reaction and heat take the soap into saponification which takes longer than HP. It is generally easier to do swirls in CP. With HP, you cook the soap and use the heat from the cook to start and complete the saponification process and the process is much quicker than with CP. An advantage to HP is that eos and fos, are added at the end of the cook and are not affected by the saponification reaction. You can also more easily do a superfat with HP by adding additional oils and butters after the cook. HP can be used sooner than CP. CP needs to cure for a few weeks but HP can be used pretty much right away. However, all soaps benefit from a cure.
I wrote this out awhile back in another thread so i went to go find it.
I started with HP soaps, and I'm glad that i did it.
You can use the soap as soon as it is hard. But it should have a little dry down time. Your better off using a loaf mold with hot process soaps because it has the consistency of mashed potatoes. And even when it's done you still have a bar of soap that is softer than a cold process soaps. (this includes even when a bar has been sitting for months, it's still softer because of the process in which it was made.) So you also use it up faster than a bar of cold process soaps. The coloring is also darker with hot process soaps because of the heat applied during the process.
If none of those issues bother you then go ahead and do hot process soaps.
However you should consider learning hot to do RTCP soap. It's actually so much easier and nicer as well. This stands for room temperature cold process soap. Basically you mix up your lye and liquid solution and wait till it's absolutely room temp. I've even mixed it up several days ahead and used it days later. Then weigh out your oils and blend them with a stick blender while still room temp. I do suggest warming hard butters like cocoa butter separate just to make it easier to work with. Then pour in your lye liquid solution and blend with a stick blender. Once you have trace add in any fragrance oils or other additives you want to add, and pour into your molds. If your making a milk soap the coloring has a better chance of staying lighter depending on the fragrance oil being used. Some scents such as those that contain vanilla will darken the soap. I really like this process and find it a whole lot quicker and easier.
Once the loaf is hard or it's hardened in individual molds I've removed it and cut it. I've waited a couple of days before testing and found it a bit soft a day or two after it's made but it made a much nicer bar than hot process soaps. Then let the rest of the batch go through the rest of the dry down time to evaporate the rest of the liquids.
Anywho i just wanted to share some of my experiences with soap, and I highly recommend cold process soap even though it takes longer. Just because you have a nicer bar of soap, and it's extremely simple when you do the RTCP soap.
on the other side of the fence, if you decide to start with cp it is always a good idea to try a couple of hp batches. because it can come in handy if you have a batch that seizes, hp or oven process ( same thing just different ways of getting there) can fix it.
like stated before. you can do any soap formula either way, hp is betterif you have a finicky fragrance, cause you add it after the cook so it isn't effected by the lye. hp gives you a sorta rustic looking bar that you can use right away if you wish but any soap gets better over time. you do the glop and mold with the finished soap where cp is pourable and the finished soap should have a smoother appearance. i have been known to use a bar of cp soap after unmolding with no problem for me, but again time makes it much better.
either method results in soap in the end. it is just a personnal preference regarding the method.