I'm pretty sure hotmail/live/premium whatever you want to call it, will not push to the handset. Even if you try to forward it to another email it must be a msn product which i've never been able to get to work either. I was so fed up with hotmail that I switched to gmail and it work perfectly.
I had the Hotmail Plus service because I was told it was required to be able to be pushed to my Blackberry. However I just got an email the other day saying they were reworking how they did hotmail email and that it wouldn't push to phones anymore. You could only get it through some proprietary software that microsoft was offering. I canceled my Plus status after that.