When taxiing into any headwind component (including a quartering wind) you should use up elevator on most general aviation aircraft.
On a tailwheel aircraft, keeping load firmly on the rear wheel helps provide directional stability and reduces any tendency to pitch forward on braking or when negotiating uneven ground, which in severe cases could risk a prop strike.
On a tricycle aircraft it is less of an issue. However, there is still some benefit in that it reduces the load on the front wheel/strut. The pair of rear wheels/struts are usually stronger than the front (as the rear pair are designed to take landing impacts) and so it is preferable to distribute more load to them, particularly on uneven surfaces.