No, you would have to use Dropbox or similar. If you have a hotmail/live account, Microsoft are integrating it with your Skydrive account and large files will automatically be shared. There is a Skydrive app for OS X as well.
Use icloud.com instead of me.com for web email. There is a Windows client for icloud.
https://support.apple.com/kb/DL1455I found MobileMe very useful, but iCloud has added a bunch of features I don't need / use and removed all the ones I found useful.