Hi Wendy! No, hot process soap and cold process soap both make very nice bars of soap.
If you use the traditional hot process method, then your bar will look a little more “rustic”, whereas the cold process has a smoother finish.
If you look into fluid hot process method though, you can make a smoother looking bar of hot process soap.
Both hot process and cold process will need similar cure times to be at their best, so just pick whichever way makes it more fun for you to make soap! :)