In most helicopters, the wind direction when hovering is of concern to the pilot, as is which way you turn when hovering.
The following applies to a single rotor helicopter with the tail rotor mounted on the left and the rotor turning counter-clockwise. The opposite applies to clockwise rotating rotors and mounting the tail rotor on the left versus on the right would take more pages of text!
Hover with no wind.
As the rotor rotates counter-clockwise, the torque reaction on the fuselage wants to turn the nose to the right. The tail rotor "pushes" the tail to the right to balance this torque. It is by varying the angle of attack of the tail rotor that we can change the amount of thrust from the tail rotor and therefore have yaw control.
The tail rotor is no different to the main rotor, it just operates in the Y axis rather than the Z axis and is subject to vortex ring state.
The vortex from the tail rotor is to the left. If the helicopter is yawed right, the tail moves left and the tail rotor moves into it's own vortex causing a reduction in angle of attack and therefore thrust. If the turn is too fast, this reduction can lead to a loss of tail rotor effectiveness.
Also in a no wind hover, the vortex from the main rotor is forced downwards.
All of what follows is for a counter-clockwise rotating rotor and applies to all single rotor helicopters.
Hover with the nose into wind, but not with enough wind to generate
effective translation lift.
This state is more or less the same as for a no wind hover and is the easiest (and therefore preferred) direction in which to hover. Turning the aircraft has the same risk as in a no wind hover in that turning too quickly to the right can lead to loss of tail rotor effectiveness.
Hover into wind with enough wind speed to generate translational lift
(let's say about 15 kts)
Now things start to get interesting. If you turn to the left, the vortex from the front edge of the main rotor is blown backwards by the wind across the tail rotor and causes a decrease in the angle of attack of the tail rotor blades since the wind from the vortex is blown on to the right hand side of the tail rotor. Therefore, a lot more left pedal is required as the helicopter turns from 0 degrees (relative to the wind) to 270 degrees. As 270 degrees is reached and passed, the vortex is no longer interfering with the tail rotor and the angle of attack for the same pedal position is increased. If the same pedal input is maintained, the rate of turn will increase rapidly and if not corrected, can lead to an uncontrolled spin.
If you turn to the right, the opposite happens. More right pedal (less thrust) is required in the first quadrant of the turn from 0 degrees to 90 degrees since the vortex is blown into the face of the tail rotor causing an increase in angle of attack and therefore greater thrust. As the nose passes 90 degrees, the angle of attack decreases and left pedal must be added to prevent a sudden acceleration in yaw.
You should be able to see that the amount of pedal required changes as the turn continues and without constant adjustment, a steady turn cannot be maintained and with enough wind, and a pilot who is not quick enough on the pedals, control can be lost.
Now let's take the turn out of the equation and consider steady hovers in wind that is not "on the nose".
Wind from the left quarter, i.e. 270 - 0 degrees. This is effectively the same condition as that first quarter of a left turn with wind from the front.
This is the difficult one. Wind is never constant. It is always changing slightly and turbulent. As the main rotor vortex is blowing into the tail rotor, the tail rotor is operating in a very turbulent and unpredictable environment. Rapid and constant pedal inputs are required to maintain control. Any deviation not caught immediately can lead to a loss of control. It is very difficult to hover with the wind from the left quadrant and is therefore usually avoided.
Wind generally from the left (a left crosswind)
As the wind is blowing into the face of the tail rotor, its angle of attack is reduced as the airspeed through the rotor increases. This can lead to the loss of tail rotor effectiveness or even a stall of the blades as the angle of attack exceeds the critical angle.
Wind from behind.
The primary effect here is the tendency of the fuselage and vertical stabiliser to "weather cock" the aircraft. It naturally wants to face into wind. If a yaw begins and is not immediately corrected, due to the effects above, the yaw can increase rapidly and suddenly. Additionally, the wind is never constant and varies between passing to the left and to the right of the tail rotor. Therefore, hovering downwind needs immediate and constant corrections to yaw.
Hovering into wind is very much preferred and is always chosen unless operations require something different. Hovering with the wind from the right is the next "most" preferred position with quartering winds from the left and hovering downwind to be avoided if possible.
All of this said, it's a standard part of training to learn how to hover in these conditions and how to maintain constant rate turns. It does require a lot of learned skill and you must be quick and accurate on the pedals with constant corrections.
Incidentally, early models of the UH-1 were particularly difficult to handle in certain wind conditions and the tail rotor was moved from the right to the left on later models to improve handling.
In a light helicopter with little power reserve, e.g. the R22, hovering in strong gusty winds is an intense part of operations. I had some close calls when learning how to do this including a loss of control which I only recovered by pulling in power and accelerating into forward flight. Not good on an airfield with other aircraft operating since my "low hours brain" focussed only on regaining control. I am ashamed to say that looking around took second place but I did learn an important lesson and with hindsight, the right thing to do would have been to land and discontinue the flight as the wind got more gusty.