Remember the bigger you go in wheel size (unless you buy very expensive light weight ones), the heavier they are.
It might only be a few pounds more per wheel, but you are increasing the "rotating mass" and it is "unsprung weight".
To put it in perspective, rotating mass (such as a wheel or brake rotor) is roughly three times harder to accelerate than sprung weight (such as the additional weight of a passenger seat).
What this means is that for every extra 10 pounds of weight per wheel it would equate to almost 120 pounds of sprung weight gained on the car.
Your acceleration, 0 - 60 and 1/4 mile times will be slower if you go from 17 inch wheels to 20 inch and the wheels are heavier.
I would not recommend going greater than 19 inch if you don't want performance to suffer.
I'm running 20x11 rear and 20x9.5 front. They are lighter than the OEM wheels that came with the car. You just have to do your research and look at the specifications for any wheel you are considering. The manufacturing process and the materials used, make a big difference in wheel weights and strength, and of course price.
I bought the standard 17" sparkle silver wheels with my car, and shod them with Nokian 235/55 R3 rubber. I still found the car a little squirrelly in deeper snow, typically plowing the front end in a corner. I would not recommend going to wider tires. Originally I was contemplating 225/60 rubber but decided on the stock size as I drive much more on dry roads than snowy here in Toronto. Also the big rubber will be significantly more expensive, unless you're not worried about cost. If you've got a PP car, the above will not work as the 17" rim won't clear the brakes.
On my 15 Ecoboost i went with 225/55-18 Dunlap Winter Maxx for my winter tires, see the Competition Orange Ecoboost below. These tires were studdable winter tires that had a very aggressive tread that were a beast in snow but they were noisy on pavement and the handling was a little mushy.
The 15 was totalled with the winter tires on the car so i wound up with a set of PP wheels in the garage. For my 17 i decided to use my extra set of PP wheels for my winter tires. I purchased a set of Yokohama Ice-Guard studless winter tires in the stock PP size of 255/40-19, see tire stack. These aren't as good in snow as the Dunlaps but are much better than an all season and are quiet and handle very well on pavement.
I am much happier with the Yokohamas because where i live south east of Boston the roads are only snow covered for a day or so after a storm and i have a beater 4x4 Pickup with the most aggresive winter tire you can get, Firestone Winterforce, for the bad days.
Why don't you get winter tires for the stock wheels.
I had a 2015 EcoBoost with performance package and it came with 19 by 9 in wheels. you might consider that size wheel and get Summer only tires are high performance tires for the summer.
I believe the 10 and a half inch too wide for the front will only fit on the rear.
You can actually fit a 10.5 up front, but only if the offset is right. Also, it depends on the tires you wrap them with. Different sizes and even brands have differences in the amount of sidewall protrusion with respect to the outside edges of the wheel, both inboard and outboard. There was even a guy on M6G that managed to fit 11's up front, but with a bit of modification.