Why do Anhingas spread their wings?
The answer may surprise you -- it has nothing to do with oil glands or wetness.

The structure of cormorant and Anhinga feathers decreases buoyancy and thus
facilitates underwater pursuit of fishes. Hence, their plumage is not water-repellent,
but "wettable."
It has been suggested that the functions of the spread-wing postures in
these birds is to dry the wings after wetting. Biologists once thought that
deficient production of oils from the preen gland necessitate wing-drying
behaviors.
We now know, however, that the degree of waterproofing of feathers is primarily
due to their microscopic structure, not to their being oiled. In addition
to helping wing feathers to dry, other suggested functions for these postures
include regulating body temperature (thermoregulation), realigning of feathers,
forcing parasites into motion to ease their removal, and helping the perched
bird to balance.
Spread-wing postures may serve different purposes in different species.
Anhingas, for example, have unusually low metabolic rates and unusually
high rates of heat loss from their bodies. Whether wet or dry, they exhibit
spread-wing postures mostly under conditions of bright sunlight and cool
ambient temperatures, and characteristically orient themselves with their
backs to the sun. Thus, it appears that Anhingas adopt a spread-wing posture
primarily for thermoregulation -- to absorb solar energy to supplement their
low metabolic heat production and to offset partly their inordinately high
rate of heat loss due to convection and (when wet) evaporation from their
plumage.
Cormorants, in contrast, apparently use spread-wing postures only for drying
their wings and not for thermoregulation. Although cormorant plumage also
retains water, only the outer portion of the feathers is wettable, so an
insulating layer of air next to the skin is maintained when cormorants swim
underwater. The difference in feather structure may explain why cormorants
can spend more time foraging in the water than Anhingas, and why cormorants
can inhabit cooler climes, while the Anhinga is restricted to tropical and
subtropical waters.
source: The Birder's Handbook, Simon & Schuster, 1988, pp. 25-27