Well, by the book, ice cold is for going aggro, full stop. Stat swapping moves explicitely say for which basic moves you can do it, it's not "use cool instead of hard whenever it's convenient". Expect your battlebabe to suck at leadership — hard is their dumpstat.
(I feel it's kind of the point. Battlebabes are free and unburdened but don't handle responsabilities well, stick them a gang and things go sour — unless they get their shit together about that, maybe by changing playbook.)
Now, you can micromanage your gang. Manipulate them, go aggro on them, seduce them, talk them into it, whatever. Leadership and pack alpha gives you, say, macros you can use some times (when your gang fights for you, when they as a whole don't do what you want) and they make things easy for hard people, but you can manage without.