The bow energy efficiency and its mechanical operation will be affected by temperature and hence so will the arrow launch speed and other relevant properties. A recent book on Olympic style archery by a top class coach suggested that the equipment set-up would need modification if the temperature changed by more than 10 degrees centigrade.
In flight, the arrow is affected by aerodynamic drag. The drag is dependent on the fluid (air) density. The higher the density the more drag to slow the arrow down and the feathers (fletchings) become less efficient at stabilizing the arrow flight. [Editor: cold air is more dense or thicker than hot air.] So factors like temperature and humidity will have a measurable effect on arrow flight behaviour including speed. The higher the temperature the lower the drag so less speed loss and a larger maximum range.