I only connect my DAW when I want to update things or install new software. I built this machine specifically for audio and have a laptop for my general intertubing (which I can keep in the room with my as I work at the DAW if I want to research something or get the ole intertube itch).
When I DO go online though I turn my antivirus back on BEFORE I plug in my network cable (I specifically did not install a wifi adapter on the system) then the first thing I do is update the antivirus. Then I'll update Windows (particularly the security updates). I may also do a quick scan of the system.
My internet settings are set to the maximum protection levels and I use NoScript and Adblock+ in my browser which blocks EVERYTHING except the bare bones of a website. I only enable scripts absolutely necessary to accomplish my updates. It's all the third party domains that allow the virus and nasty critter to creep in (at least on trusted/secure/reputable sites).
Before I download anything (but sometimes after and before I install) I create a Windows system restore point so if something wonky happens I can get back to where I was (much quicker than system image and doesn't require a huge chunk of storage space... but not as resistant to full on failure).
Paranoid? Hellz ya... but it's the internet. Things happen and even the "trusted" software manufacturers put all sorts of dumb crap that auto connects to do "helpful" things. When I'm at the DAW I'm doing music stuff and I expect the DAW to focused on exactly that. Not pissing around in the background having a little chat with god knows what server.