The easist thing to start off with is to check your mail fetch settings.
HT4146 About cellular data usage has step by step for a setting up your fetch settings.
Basically you want to do this:
Settings > Mail, Contacts, and Calendars > Fetch New Data >
Ensure that "Push" is enabled, I think hotmail supports Push now.
Then below, see Fetch:
Set to a time you think is good for you, remember, more often means more battery usage.
Then below that: see Advanced,
Click into that, and click "Gmail" and ensure that is set for Fetch and not Manual.
Another article sugguests that you may also need to register the device with Hotmail.
I hope this helps.