Coolant reduces the temperature of the cutting zone which will impact tool life. It may also allow you to run at a higher stable spindle speed than if run dry. It does not change the stiffness of the tool or the frequency at which it vibrates, so the stable speed zones and maximum stable depths of cut are not changed by the coolant being off or on.
In the case of tools with coolant through holes, whether or not coolant is running through them will not change its stiffness. Tools with holes will holes will have slightly less mass than identical tools that are solid, so there may be some difference there.