IMO you would be extremely unlucky to strike weather to close roads, especially that early in winter. Good on you for wanting to goto MT Cook, I was like your friend having lived in the SI and never been there till last year and it is truly amazing and well worth it! It's a hard a choice choosing between over thing at MT cook village or Pukaki as they are both equally amazing...whatever you choose you won't be disappointed. I can recommend the Hermitage, it is amazing! Milford Sound to Mt Cook will be a long day, so I suggest leaving early so you can have regular stops at points of interest along the way...be warned, there are many!

I wouldn't bother with the west coast....chances are it will be raining and if you head into Mt Cook there are plenty of glaciers to see there and it isn't that much different...

I have only done Abel in summer so can't really comment on it sorry...it's a spectacular walk though!