He was doing a 'snow job' : A snow job is an attempt to persuade or deceive someone, especially when flattery is used.
In your example, this Stradlater was attempting to convince this girl she had found a real gem, a soft, sincere, and genuine guy. Coupled with his good looks, he hopes to have her as putty in his hot pawing hands.
I hope her father had warned her of such Lotharios.
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