With a dry or purely wet road, a slick will give maximum contact area. You will not get aquaplaning with bicycle tyres, since you need to do something like 120mph on bicycle wheels to get this effect!
Once you add in contaminants like gravel, mud, and oil it becomes a whole lot more complex, and some grip may help, but to what extent is going to be variable and will largely depend on the degree of additional material. Obviously off-road riding will need a lot of grip, but when there is some loose stuff on an otherwise solid roadbed, what degree of grip is required is going to be a very personal choice.
For ice at least, studs will largely solve the problem, although the exact degree is again likely to depend on other complex factors such as thickness of ice, presence of snow, and stud distribution over the tyres surface. Ice tyres seem to favour studs off of the centreline, to aid cornering without impacting straight line rolling resistance. Those tyres designed to deal with snow as well tend to have more grip (like MTB tyres) to help with traction in the looser material.