I am a "Southtowner" and don't have snow tires and have never had four wheel drive/AWD. Orchard Park often gets more snow than the city, but it certainly does not get the volume of snow that say Ellicotville gets. I think the snow you are referring to is actually a bit further South ... Boston/Colden/Springville and points South see much more snow than the city itself. Keep in mind that the snow off the lake often travels in bands, so an area just a few miles away can get quite a bit more/less snow than wherever you are located. Don't fret as the major thouroughfares are usually kept quite clean even in the midst of a storm. Enjoy your visit!
I just noticed you are from Syracuse....you should be more than fine. Syracuse gets more snow than Buffalo!!!