We all know that what you call a cold burn is very rare and maybe never done. Most burns are done when birds still have their nests, and the young are not able to yet fly or have not yet hatched. There are several species of birds that nest on the ground, and they need their nests for protection from the weather. Then you have the rabbits and other animals which can quickly spread a fire to where it gets out of control. Land that is burned repeatedly has a tendency to get hard because the organic mater above and below the ground is burned. Hard ground does not absorb water as well. The result can be more runoff and less water in the soil for the vegetation.
OFF-Vet is correct on having a good balance with other animals in addition to deer, but I would do what I could to discourage it being good habitat for coyotes and wolves. Cattle and sheep will eat weeds and plants that deer choose not to eat. Goats can do a very good job of eating down even large weeds.