There is absolutley nothing wrong with thawing it completely, skinning, cutting, and re-freezing it. We have done so for years and have never noticed a difference between those that were frozen, thawed and cut and those that were cut fresh. (As long as they were frozen with the hide on or quartered wrapped and frozen.)
If you think about it, which one would really be fresher? One that was frozen right away thawed and cut or one that was left hanging without freezing for a few days and then cut? In my opinion the one that was frozen and thawed would be the "fresher" deer. Leaving a deer hang for extended periods without freezing only increases the bacteria count and moisture loss, and lessens the quality in my opinion.
Dave