Even shutting down the account might not help. Somehow, your list of Hotmail contacts found its way to a computer or person who creates spam. That's already done, so deleting the Hotmail account won't prevent the existing list of contacts from being used for spamming, nor will it prevent someone from spoofing your Hotmail address.
You can tell all your contacts that e-mail spam is being sent to them outside of your control. You can change your e-mail address and ask your contacts to simply filter out anything from the old Hotmail address. These are just workarounds, though. The spam is likely to keep coming.
You can try changing your Hotmail password, in case some person or bot is signing on to your account and sending spam to your contact list. You can scan your own computer carefully for any viruses or other malware that might be using your computer to send e-mail to your Hotmail contact list without your knowledge.
These days I have a long list of filters that examine my incoming e-mail, as I get several thousand spam messages per day. Sender addresses that are in my address book get through, and usually that's not a problem. However, I started getting weird spam from someone who was in my address book a few weeks ago, and since I had no easy way to authenticate e-mail from her and had not received any legitimate e-mail in a long time, I reluctantly had to drop her from the address book. It's not frequent but it happens.