Trade in my current car, or hold on to it and continue on my current loan?

Financially it would be a dumb idea to trade it now. Although you are worried about the value dropping, you don't have any equity to loose. Drive it for another 3 years, and even if it somehow dropped to a $1000 car, you wont be any worse off.

In fact if you keep it, pay it off, and you end up owning a still good Corolla. Look up the value of a good condition 6 year old one right now. Even if it's dropped to only $7,000, that's YOUR $7K equity.

Or trade it, start a new loan from zero deposit again, and in 3 years you will be in exactly the same situation again, and still actually own pretty much nothing.

The car you have is still effectively "brand new". It should be good for 200K miles, and at least 10 years, more if the mileage is reasonable.

Now if you NEED 4WD, that's different. You could probably trade with no difficulty, but financially it's NOT a good idea.

The lower mileage would help a bit but you're still dealing with a 2 year old car and depreciation is the steepest the first 3-4 years. Financially speaking, it's a bad idea.

Have you invested in a quality set of winter tires? If you're still driving on all-season tires in the winter, that would be why you're having trouble with hills. A full set of winter tires mounted on their own rims is a lot cheaper than the big hit your wallet would take trading in the car.

That car with a good set of winter tires should handle better in snow than about any AWD car with factory all seasons. I live in the middle of the NE Ohio snowbelt and often get places using snow tires on a front-wheel-drive car during times people with AWD couldn't make it. Of course I drive differently than at other times and pay attention to how the car feels. Anyway, I also recommend keeping the car and getting winter tires. And, if possible, saving enough to pay off your loan early and building up a savings.

Let's make one thing clear. If you trade your car in now, you will absolutely get ripped off. Dealers eat, breathe, and sleep thinking of ways to screw you. I know this because I used to sell cars. Stick with what you have until you get it paid down enough so you're not upside down. Then decide what you want to do. But whatever you do, do not ever "trade" your car in at a dealer. You will likely get several thousand more selling it on Craigslist. I know this because I had my Jetta appraised at CarMax for $4500, I proceeded to sell it on Craigslist for $6900 in less than 2 months.

Keep your car, you don't want to take another $10k bath do you ?

Use snow tires or chains if you really need them. lots cheaper than a new car.

I'll just add that while AWD helps you get moving in slippery conditions, it doesn't help you stop any faster.

Keep the Corolla and purchase snow tires for the winter months.

Hold on to it, get snows on all four corners, and call it a day.

i can't belive you are having handling issues in winter. use proper winter tires and be prepared to drive slower.