Using cyclocross tires for winter riding I've currently got a fixie road bike with some stock road tires. They're fairly low-profile, as in, they aren't knobby, and have low-profile treads.

Because my fork and stays have enough clearance for it, I'm debating using some CX tires at least early in the winter, before riding becomes nigh impossible altogether.

The two biggest environmental hazards I'd be trying to work around would be the cold (I want to try and stay on the bike down to about -10 or -15 ºC) and slush, which is extremely abundant where I am even fairly early on in the season.

I'm not looking to avoid ice; at that point I'll probably look for another means of transportation.

Are CX tires generally alright for winter riding? What road conditions would limit their effectiveness?
Considering that you will be hanging up your bike come ICE time... I would say that CX tires can/would be a bit more confidence inspiring that a typical slick tire.  However, I don't think that a CX tire would be much better (and likely more expensive) than a nice inverted tread commuting tire like the continental Touring Plus or an equivalent.

Having commuted in an area like you describe... cold wet, more slush than snow, etc... I have had very good luck with inverted tread commuting tires and they can be (are) usually a bit more pleasant on pavement than CX tires.