He was snowing hell out of her

[Tdol]

Thanks for that.

[5jj]

In the meaning I first met, it seems to date back to 1943: Snow job - Definition and More from the Free Merriam-Webster Dictionary

The Tony Snow version is here: Urban Dictionary: snow job

[Nersi]

Read the text below :

I kept laying there in the dark anyway, though, trying not to think about old Jane and Stradlater in that goddam Ed Banky's car. But it was almost impossible. The trouble was, I knew that guy Stradlater's technique. That made it even worse. We once double-dated, in Ed Banky's car, and Stradlater was in the back, with his date, and I was in the front with mine. What a technique that guy had. What he'd do was, he'd start snowing his date in this very quiet, sincere voice – like as if he wasn't only a very handsome guy but a nice, sincere guy, too. I damn near puked, listening to him. His date kept saying, "No – please. Please, don't. Please." But old Stradlater kept snowing her in this Abraham Lincoln, sincere voice, and finally there'd be this terrific silence in the back of the car. It was really embarrassing. I don't think he gave that girl the time that night – but damn near. Damn near. (7.40)

It seems to be sexually over demanding or making advances in a way that leaves your victim speechless or unable to protest by behaving courteously or flatteringly.

Snow the Hell out of seems to intensify the act.