If lowering the temperature is the only change in conditions, then you would not expect a protein to denature. However, proper protein folding depends on many factors besides temperature. Salinity (salt concentration) and pH changes can denature proteins. So you could denature a protein at...
Biology is a broader, less specialized degree than environmental science and would prepare you for a wider variety of graduate programs and careers. I would imagine that a significant number of environmental science graduate students have their bachelor's degrees in biology. At most schools...