It is the energy, heat, flowing from your hand that produces the sensation of coolness. The main reason for serving potatoes wrapped in aluminum foil is to increase the time that the potatoes remain hot after being removed from the oven. They also serve to retain moisture. In touching the tongue to very cold metal, enough heat can be quickly conducted away from the tongue to bring the saliva to sub-zero temperature where it freezes, locking the tongue to the metal. In the case of relatively non-conducting wood, much less heat is conducted from the tongue and freezing does not take place fast enough for sudden sticking to occur.
Air is an excellent insulator.
The reason that fiberglass is a good insulator is principally because of the vast amount of air spaces trapped in it. Heat from the relatively warm ground is conducted by the gravestone to melt the snow in contact with the gravestone. Likewise for trees or any materials that are better conductors of heat than snow, and that extend into the ground. The snow and ice of the igloo is a better insulator than wood. You would be warmer in the igloo than the wooden shack.