Chances are you have a summer tire on the vehicle. Check your owner's manual or tire warranty to see what kind of tire is fitted on the vehicle. Another option is to look on the sidewall of the tire then look it up on the internet to see what the deal may be. A summer tire will never do well in winter weather because of the rubber composition. A dedicated winter tire will solve your problem but that may not be a practical solution because of the change in seasons, if you live in the area of the country that has 4 seasons. The simple answer to your question is that it depends on the type of tire and if its suited for the type of driving you expect. One of the better winter tires is Blizzak. If they make a 20 inch tire they would be an excellent winter tire. Blizzaks are a dedicated winter tire only.
All else being equal, wider tires are better on warm and dry surfaces for grip but worse in rain and snow.
Of course there are many variables when it comes to traction so the above is a very generalized statement.
It may have to do with the actual rubber composition. Just because the tire looks good and is wide doesn't mean the rubber will have sufficient grip. Find a review on the particular tires to see what its performance - or lack of performance has been found to be.
Grip on dry pavement is better with a wider tire, but worse on snow.
Try 5/10, maybe 6/10 is too much. I don't know how you measured that. Why do you want to abuse the vehicle anyway?
The narrower the tread bars the more weight on the bars and more traction.
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We have a Mazda CX-9 GT with 20 inch wheels and 245mm tires. We have noticed that the car isn't too grippy. Like if we launch the car, even at 6/10 gas pedal press, it'll launch with bad traction. The normal 0-60mph of this car is 6.5-7.5sec. It has AWD and traction control too. Is this supposed to happen? If I add 285mm tires will the grip be better or will it just make things worse?