Some deciduous trees don't always entirely shed their leaves in Winter months. This is known as marcesence, and is found in several tree species such as the Oak, Beech, Musclewood, Ironwood and Hornbeam.

Marcescence is the retention of dead plant organs that normally are shed. Trees transfer water and sap from the roots to the leaves through their vascular cells, but in some trees as autumn begins, the veins carrying the sap slowly close until a layer of cells called the abscission layer completely closes off the vein allowing the tree to rid itself of the leaf.

Source : Wikipedia

The reasons for marcesence are unclear. Theorists have suggested :

• It may deter herbivores from eating the trees' twigs over Winter
• Shedding the leaves in Spring may provide nutrients for new growth
• Keeping the leaves could increase the speed of decomposition
• It may allow the trees to trap snow for moisture