** Revised based on comments
We are planning a road trip from Washington DC to Quebec City around the 3rd week of December, following the route prescribed by Google Maps (broadly, Interstate 95 to NJ Turnpike to I-95 to NY Route 17 to Interstate 87/Autoroute15 to Autoroute 20).
My question is, during that time of the year, how safe are the roads for driving, considering inclement weather, such as snow storms?
A simple rule: check the weather regularly, and find a place to stay before it starts snowing.
Once the storm is over, the road crews will have the highways cleared within a few hours. And if you wait until traffic starts to crawl, you will probably find that there's no place to stay.
While people from northern states like to think of themselves as competent drivers in snow (and I'm one of them), it's a myth (in large part because the road crews do such a good job of clearing the roads that most people never actually drive in a storm). Plus, major highways are filled with people who are not from northern states. Everyone slows down, a few people slow down too much, queuing theory rears its ugly head, and traffic comes to a near standstill.
An anecdote: there was a pre-Christmas storm in 2004. A friend and I both left Philadelphia on the afternoon the storm was forecast, following the same route through Ohio (he was going to Cleveland, I was going to Ann Arbor MI). I got a room in Pittsburgh, he went straight through. The snow started 20 miles from his destination, and it took him several hours to cover those miles. In the morning the roads were clear (although the medians featured overturned tractor-trailers).
And a word of advice: keep a sleeping bag in your car. Just in case you decide not to get a hotel room until it's too late. If you have to sleep in a rest area or parking lot, you don't want to risk either CO poisoning or running out of gas due to leaving the engine running. Even a midweight bag is comfortable in an enclosed car (here again, I speak from experience).
There may be a lot of snow, and expect some snow anyway.
I remember doing a similar trip around Christmas 2010. There was a big snowstorm right after Christmas and almost no bus would drive us from Philadelphia to New York, and some friends doing it by car were slowed down because of it.
Anyway, Quebec City has a lot of snow anyway (you can see the snow report for Montreal, on the way) so there will likely be snowfalls around that time of year. However, unless there is a particularly big impact like in 2010, the roads are usually well maintained and snow is removed within the following hours.
I do not know exactly what you are asking for (do you want to know if it implies delays or if you should have adequate equipment?). But there might be some to much snow and it might result in delays. You should probably have snow tires, and having chains in the trunk might be helpful (but I do not think you will necessarily use them).
Generally speaking American and Canadian roads are fairly well cared for in the winter. Interstates and Autoroutes even more so than smaller rural roads. The only time I'd be worried (I live in the greater DC/Northern Virginia area) about making that trip, even in my own Mustang, is during an actual snow storm/blizzard. Even then, I'm originally from Michigan and I'd just use my wife's car instead and go for it. Driving in the snow, for me, is relaxing.
Also, there are three things to worry about in the Northeast US. Snow drifts, drifting snow (not the same thing) and ice. If it is snowing faster than the plows can keep up, you'll get drifts. They will be impassible by a normal 2wd vehicle. Drifting/blowing snow causes blindness of the road and an inability to see the roads sides (whiteout). Pull over until the winds subside. If it is warm enough for ice, the plows will be dropping ice melt (colloquially 'salt') and the roads will probably be more wet than slick. Good luck with your trip and make it an adventure. Pack well, dress warm.
Finally, The Weather Channel is your friend.
Unless your driving in a snow storm, the road are usually we cared. For the Autoroutes in Quebec, check the Quebec511 website. It will give you the road condition, visibility condition and any problem, like road closure, in real time.
For added safety, you should put winter tire on your car, it will give you a better adherence to the road. Also be sure to use winter windshield washer fluid, you don't want it to freeze on you windshield or in the tube. I also recommend that you have a spare canister, you can use a lot depending on the road condition (wet or dry).
Since you are going to Quebec city in winter, be sure to bring warn clothing, the temperature can drop to -40. On a side note, if you have time, go try the toboggan ice slide at the Chateau Frontenac.
