How to slow player on x and z

OK, I thought your character can't control its movement when falling.
In that case, still separating the case when you are falling and when not, you can try take the horizontal speed, limit it, then add back the vertical speed. Something like this:

 private void LimitSpeed (Vector3 velocity) {
     if (falling) {
         float verticalSpeed = velocity.y;
         Vector3 horizontalVelocity = new Vector3(velocity.x, 0, velocity.z);
         // limit horitontal velocity
         limitedVelocity += verticelSpeed * Vector3.up;
     }
     else {
         ...
     }
 }