How do the actuator loads (e.g. for the ailerons) vary between different flight phases?
Indeed the hinge moment equation is (with index $_s$ for surface) 
$$H_s = C_{h_s} \cdot ½  \rho V^2 \cdot  \delta_s \cdot S_s \cdot \bar{c_s}$$ 

The moment coefficient $C_{h_s}$ depends on aircraft angle of attack, surface deflection (!) and trim tab deflection, as depicted in the figure below (from this answer). It is not a simple constant linear function due to shading of horizontal tail in the flow of other bits of aircraft structure.



So of course, hinge moment calculation depends on aeroplane configuration and geometry. But as @JanHudec mentions in a comment, the two main variables here are dynamic pressure and surface deflection.

Full surface deflection at cruise speed results in the largest hinge moment. It may also result in structural forces higher than the limit design forces, for instance load factors > 2.5g. It would be safest if the actuator force can never exceed the hinge moment required to reach maximum load factor, which would require making plots of (hinge moment for max. load factor) vs. airspeed, at different c.g. at maximum weight.