All though it is tempting with the cold temperatures we are having, feeding wildlife this time of year can have some very negative consequences for the animals.
There is food out there, but the animals do need to work a little harder to obtain it. The natural food sources are also not as rich in nutrients as food they might find in the summer or fall. The sudden nutritional richness of food that we as humans might provide such as corn for deer can cause them to get very sick or die.
Ruminants (such as deer, cows, goats etc.) in general are sensitive to rapid changes in their diet. These changes can cause a condition called acute rumen acidosis.
This condition is caused by the rapid fermentation of starches (like the carbohydrates found in corn) in the rumen (1st of 4 stomach compartments), which causes the rumen pH to drop rapidly. This sudden pH drop causes excessive lactic acid production in the rumen, which causes the rumen pH to drop even more. Unless we as humans intervene medically the animal will die.
You can see that a deer that has been getting by on eating pine needles and dried weeds would be very attracted to a rich food source such as corn and could easily overeat and die from acute rumen acidosis as a result.
This actually happens sometimes without direct human interference when deer get into a harvested farm field and overeat on grain that was spilled.
Keep in mind that you have no way of knowing if you are the only person feeding these wild animals making quantity consumed difficult to judge.
Other non-ruminant species of wildlife can get similar conditions which all can result in organ failure and death. In wildlife rehabilitation we are very aware of this and we utilize carefully designed protocols that involve hydration therapy and carefully introduced chosen or formulated food sources.
Another consideration would be for the food that we provide to sit too long causing potential issues with mold and spoiling. If wildlife is hungry enough they might consume food that they would otherwise not consume causing illness or death. We have seen this with moldy grain consumption in geese and ducks. The geese suffered from elevated levels of mycotoxins (poison produced by molds) and it caused a large number of them to die.
We also have to keep in mind the carrying capacity of a habitat. We as humans have greatly reduced the habitat of many wild animals. This means a larger number of certain animals are required to utilize less space. We need to let what habitat is left dictate how many animals of each species it is able to carry. If we further upset the balance by supplementing food, a larger number of certain species will congregate in an area causing more vulnerable flora and fauna to disappear or simply die and causing long-term harm to the habitat, which might cause that habitat to become inhabitable. Think of overgrazing causing desert like conditions.
If food becomes scarce, wildlife will disperse and venture out to find other areas where there is still food, which is the natural balance of things. Think of Canada Geese flying south for the winter. That behavior in geese is partially prompted by food availability combined with the availability of open (non-frozen water).