You need to delete your current hotmail account set up on your iphone.
Once this has done click 'Add Account' and select the new 'outlook.com' tab.
Set up your hotmail account again from scratch and this will then allow you to select how many weeks/months of emails you sync to your phone.
Im not sure if anyone else had a similar problem to me prior to iOS 7, but if i deleted an email from my hotmail account on my iphone - it wouldnt sync with my actual hotmail account. So when i logged in online all the emails I had deleted on my phone would still be showing as unread.
But by setting the account up as above, they now sync perfectly.
Well for me anyway 😁