I kind of like the idea of taxing tires. Tire wear corresponds directly to road wear, when you take into account the type of tires (e.g. studded vs. non, what sort of loads they're designed to bear, etc). The only issue is that due to how expensive tires would get, it'd be a significant counterincentive to people replacing them at proper intervals; you'd have to significantly tighten enforcement on that.
It seems like a combination of vehicle mileage and weight are the most fair method. Tire taxation has other flaws outside of creating a disincentive to proper maintenance, such as better-handling tires wearing out disproportionately to miles driven, etc. (ulta high performance tires are notorious for this characteristic)