Cold Approach isn't the same as Dates.
If the chick wants to go out on a date with you (either because you initiated, or she did) - the fact that she's interested in the date tells you that she is attracted. Doesn't mean it's a home run, or you just met your future wife. It just means that she got a thin slice of who you are, and she wants more. The date is basically her "interviewing" you. That's the frame that she often adopts.
That said, your frame is the same. You're not trying to sell yourself. You're trying to evaluate her. Plenty of guys have had their lives ruined because they wanted a sex partner, or just someone to be with them and stop the loneliness.
In practical terms, your job at that point is to deepen the attraction, build trust, get a bit of arousal going, and escape the public venue to a one that's more private. (all of which are described in a billion other posts on this forum and in the GC articles - so don't ask me)
Know what your goals in general, and with the particular girl. And design the date around those goals.
One of the good things about going out on a date, is that once you get past the first few moments of a date where it's stranger talking to stranger in a formal way, you'll get into a conversation with someone that wants to talk. From this experience, you'll know during your cold approach what a girl that is actually interested in YOU really looks like. You'll also take note of how you feel emotionally.
One thing I would avoid doing on dates, is making the date meta. There is part of you that wants to know how to cold approach, how she gets approached, why she picked you, how the date is going, etc. Do not indulge yourself by asking her. Focus on the date, on having a good time.
WIA