If the Civic had enough ground clearance and was good in the snow, pretty much any economy car will perform the same.
First I would suggest the Prius. It has gotten 5/5 reliability on 15 of the 17 years if has been on sale. Our 2005 Prius is still running at 252k miles. The 3rd gen (2010-2015) gets over 50 MPG and the battery performs well in cold weather. It has a powerful heater, though the engine has to turn on if the engine isn't warm. Ground clearance is average like your Civic. My family of four has been on several 4-day vacations in both our 2005 and 2016 Prii, so it does have a large cargo space. The rear seat is large for a compact car with reasonable width and lots of legroom, one of the reasons it makes a great taxi. With my 2016 Prius in stop and go traffic I get around 70 MPG with normal accelerations, which is around triple what you would get in your old Civic. The best model year for you is the 2012 because MPG increased and that was the start of a mild refresh when there were more standard features. Advanced safety systems were available in the higher trims. It has a comfortable ride and is an ideal commuter or family hatchback.
The Soul is another good one. It has a large cargo space, especially with the rear seats down. Passenger space is pretty good and it is available with many features for a low price. These will be cheap because Kias depreciate quickly. They are reliable, but the Prius, Corolla, and Civic will hold up a little better. If you can get one Certified Pre-Owned, you can get the remainder of the 10 year/100k mile powertrain warranty. Many luxury features such as cooled seats were available with the Soul. I would suggest a 2014 because that was after the refresh. MPG will probably only be a little better than your Civic. The Soul has never been a comfortable cruiser. It is pretty bumpy and loud.
Comparing the 2012-2015 Civic and the 2014-2018 Corolla, I would take the Corolla. These were the worst years for the Civic in terms of how Honda cheaped out, though reliability was still very good. Major selling points to the Corolla are the large back seat legroom and reliability. It is perhaps the most reliable car on the road. It rides nicely and has large trunk for the class. The engine is rough and loud when passing or merging and MPG is not as good as the Prius. It isn't available in a hatch. I have driven a 2015 and 2017 as loaner cars and they are perfect point A to B cars for most people, though they are not at all exciting. I would still take a Prius over the Corolla because the Prius does everything better (except acceleration) and MPG much better. All years are reliable, but I'd get a 2014+. I don't know if you can afford the 2016 Scion iM, which is a Corolla hatchback. It is about $1,500 over budget.
If you start to look at some overpriced SUVs, the Toyota RAV4, Honda CR-V, and Mazda CX-5 are all great choices. They won't do well on gas, though. Some other hatchbacks worth a shot are the Hyundai Elantra GT, Kia Forte5, Honda Fit (might not be large enough or comfortable), and Mazda3 (though the interior/cargo is tight, lots of fun to drive). Avoid the Focus.
Like Dan said, get snow tires and your car will almost for sure perform well in the snow. AWD doesn't help with braking or cornering in the snow, only starting from a stop. I don't agree with the 2012 cars article you linked because all cars are different and it is a generalization, not a fact. Please tell us what you buy and good luck!