http://www.waltersforensic.com/articles/accident_reconstruction/vol1-no8.htm
I bolded what I think are key points that indicate tire design and composition do affect a skid.
The Skid-To-Stop Velocity Formula
The simple form of the skid-to-stop velocity formula requires known values for the
coefficient of friction and the length of the skid marks. The pre-skidding velocity is given by:
V= / 255 m S
where:
V is velocity (km/h)
m is the friction coefficient
S is skidmark length (metres)
Coefficient of Friction
The coefficient of friction, (denoted by the greek symbol ("m ") is a
rating of the grip or "traction" between a road surface and a tire. The value of the coefficient of friction is a fraction, which must be between zero and one. The lower the value of the coefficient of friction of the roadway, the more slippery the roadway will be. For example, an icy surface may have a coefficient of friction in the range of 0.1, while a clean, dry asphalt surface may have a coefficient of friction of approximately 0.7.
Factors Affecting The Coefficient of Friction
The main factors affecting the friction coefficient are road surface texture and condition
and tire composition.
Condition of the roadway refers to the presence of snow, ice, sand and other lubricants. The presence of any of these will make the surface more slippery, which reduces the coefficient of friction.
Texture of the road surface refers to the natural roughness of the asphalt. A relatively new asphalt roadway has a "sharper" surface with a high coefficient of friction. An older well-travelled asphalt roadway has a smoother, slicker surface with a lower coefficient of friction.
Tire composition and wear surprisingly plays a lesser role in determining the coefficient. It appears as though road surface texture and condition are the more important factors.
Tests show that on a clean, dry surface, bald, worn out tires actually will skid to a stop more quickly than newer, treaded tires. However, on a wet roadway, treaded tires are preferred.
Temperature has a small but generally negligible effect on the coefficient of friction; as temperature increases, the friction coefficient reduces minimally.