I'd go with the phone call myself. You say you don't know the middleman very well but you guys all hung out on the slopes together, he probably doesn't think of you as a weirdo.
I was thinking as I was reading the thread, 'What if she doesn't reply to your e-mail?' If she's interested in you but doesn't check her mail then you'll be in limbo, where if you don't hear from her you don't know if she didn't read it or if she's rejected you.
Even if the middleman tells her 'This guy was asking for your number', she remembers how you were on the slopes, and if you make another good impression on the phone then she'll know you're not a freaky creepy weirdo. And you can get a decent 'Yes' or 'No' from her on the phone without worrying whether she's rejected you or is oblivious to all of this.
So what're you going to do now? She hasn't replied in two days, do you call her or just leave it be? If she doesn't mention the e-mail next time you see her, but is still friendly, do you ask if she got it and possibly make it awkward, or just forget it and miss the opportunity?
I say it's not too late to ask her friend for her number, give her a call and just casually mention that you sent her an e-mail but she must not have got it. Then you'll know for sure if she'll date you.
*High five*
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