Are falling objects harder to push compared to objects at rest While an object is still in the air falling under the influence of gravity, does it take greater force to push or steer it to the side compared to when the object is in a state of rest?
 A: As Galileo discovered some 400 years ago, a body's horizontal motion is independent of the vertical motion. A given resultant horizontal force acting on a falling body will give it the same horizontal acceleration (while the force is acting) as if the body had no vertical motion.
A: Yes, you might find falling objects harder to push, if you factor in the drag force. Initially, before you apply any force, the direction of the velocity is1 downwards ($\downarrow$) and the corresponding drag force acts upward ($\uparrow$), because almost all the drag forces experienced in daily life can be written as
$$\mathbf F_{\text{drag}}=-g(|\mathbf v|) \mathbf{\hat v}$$
where $g(|\mathbf v|)$ is a scalar positive function of $|\mathbf v|$ and $\mathbf{\hat v}$ is the direction of velocity vector.
Now once you start applying the force, the body starts accelerating in the horizontal direction ($\rightarrow$) and thus gains a velocity in the horizontal direction. But as this happens, the drag force also develops a horizontal component in the opposite direction to the horizontal velocity ($\leftarrow$). This opposes your force and reduces the effect of your force. Thus you might feel harder to push a falling object
Practically, the time taken by any object to fall from reasonable heights is quite samll to notcics such a difficulty in pushing the object sideways. Moreover, a stationary object, most probably on the ground, will be acted upon by friction if we try to push it. The friction is very commonly felt and is definitely much stronger than air drag in everyday life cases. If you were talking about pushing on a frictionless surface, then that is actually easier than pushing against air drag.
Note: Do see the comments below this answer, where some common questions regarding the validity of my answer have been answered.
A: Newton's second law is a vector equation $$\mathbf F=m\mathbf a$$
With two dimensional motion this gives us two equations
$$F_x=ma_x$$
$$F_y=ma_y$$
Therefore, the only way the scenario you propose can happen is if there is some horizontal force that depends on the vertical velocity $\mathbf f=f(v_y)\,\hat x$. For falling objects I don't think this is the case, even if you do consider air resistance. Therefore, I would say no, what you are asking about will not happen.
