I've been forwarding mail from GMail to Outlook webmail for some time and nothing that lands in GMail's spam folder is forwarded anywhere.
But if your Hotmail is spammed out, see if you can delete your primary account username after establishing some alias addresses as described below. If not consider upgrading to Outlook. You can change the username part of your new Outlook address and create alias addresses to foil the spammers.
Hot mail has alias addresses. If you need to receive mail from, say, old schoolmates or military buddies, post the alias on Facebook or other social media, or your website or other business media.
If you start getting spam in that alias address, send a new alias to these old friends (or new business clients) and create another alias address to post on Facebook or your website or business media.
After using those addresses for a while, delete the spammed aliases and the spammers are gone....until the next round.
To set up a new email address alias in Windows Live Hotmail:
Move the mouse cursor over Inbox in the left column in Windows Live Hotmail.
Click the gear that appears to the right of Inbox.
Select Create a Hotmail alias.
Type the desired alias under Email address:.
Click Create an alias.