We're planning on buying winter tires for our g35x (original tires are 215/55/17) but 215 seems so thin so we were wondering if 225 would be alright. Has anybody tried it? Like I saw problems like "rubbing" I don't even know what that means or if it applies but I just want to be sure it won't cause problems in the future.

You want skinny tires for winter use, Google a "tire size calculator" or use the one listed in the header for this site. There's good calculators that will display both tires side by side so you can visually see the difference.

Rubbing means exactly that, the tire can rub inside the fender well, usually during hard suspension compression like speed bump or when turning the steering wheel all the way to the lock.

I would stick to the factory tire sizes here, especially since you're talking about winter tires. Cleric is right, skinnier tires work best in snowy/icy conditions and Infiniti engineered your car to run a specific size. I don't see any positive reason to change that.