For the A320:
In case of crosswind various precautions need to be considered:
1) Avoid deflecting the stick into wind. It has practically no efficiency, but has adverse side effects on braking. Indeed, it creates a differential down force on the wheels into the wind side due to the aileron deflection, and it creates a differential drag effect due to spoiler retraction on the out-of-wind side. These differential effects favor the natural "into the wind" turn tendency of the aircraft.
2) The reversers have a destabilizing effect on the airflow around the rudder and thus decrease the efficiency of the rudder. Furthermore, it creates a side force, in case of a remaining crab angle, which increases the lateral skidding tendency of the aircraft. This adverse effect is quite noticeable on contaminated runways with crosswind. In case a lateral control problem occurs in high crosswind landing, consider to set reversers back to idle.
3) In lower speeds, the directional control of the aircraft is more problematic, more specifically on wet and contaminated runways. Differential braking is to be used if necessary. On wet and contaminated runways, the same braking effect may be reached with full or half deflection of the pedals; additionally the anti-skid system releases the brake pressure on both sides very early when the pilot presses on the pedals. Thus if differential braking is to be used, totally release the pedal on the opposite side to the expected turn direction.