I would start here:
Tire size calculator
You can plug and play and see what the OAL (overall) measurements are for a given size, including current size and the new size you want. Once you figure out the difference in diameter, you can go out and measure or eyeball the radius increase length over your stock tire and see what it hits in the wheel well.
Don't forget to turn the tire all the way left and right and measure clearances in the wheel well there as well. Remember, that you're going to be measuring by adding the radius difference vs overall difference. So, let's say that your current tire is 26" tall and new tire set up you want is overall 27". That means, there's a radius increase of .5". So, you'll need to add an additional .5 from the center of wheel to edge of tire in all directions and see what it may rub or hit.
Now, keep in mind that different tires have different dimensions, even within posted sizes. It's like shoes - just because they are a size 14, doesn't mean they will all fit exactly the same.
Additionally, snow tires generally start out with a 12/32nd of tread vs regular tires at 10/32 (for a passenger car). So you may want to think of that as well.
Tirerack.com is great at listing dimensions for each specific tire make and model.