Would you advise against driving from New York City to Quebec City in February?

Depends.

Do you have good winter or all-season tires? What kind of vehicle do you have?
Do you have experience in driving in icy/snowy surface?
Do you have to be there? If there's a blizzard, can you afford to just not go instead?

For example, if you have an important interview to go to, then please don't drive. You may be stuck somewhere. But if you're on a leisure trip and have lots of experience driving in winter conditions, and time isn't a crucial factor, then that's okay as long as you prepare yourself and your vehicle for the trip.

Thanks for the advice. I have rented an SUV for the trip. I just want to go to the Ice Hotel for the experience. Thought that I can save some money on the airfare to pay for the hotel since there will be four of us. Beside, flying is not much fun nowaday with all the hassel at the airport. I do have a whole week to make the trip and can indeed stop on the way if the driving condition gets bad. Will pack a couple of bottle of windshield fluid, ice-salt, etc.

How offen do the bad driving conditions happen up that way?

It just depends on the weather. Sometimes you get a huge snowstorm, like this weekend; sometimes you don't get anything for a couple of weeks. And the major highways usually get plowed and cleared within half-a-day anyways. Quebec City and Montreal are still just in southern Quebec, afterall.

Pack blankets, water, dry food, and don't leave the fuel tank too low.

Thanks for the advice. Now I feel better about the decision to drive. Will definitely pack carefully to include the items you suggest. Thanks again.