Absolutely fine. Most don't inject straight from the fridge, because they have the opposite reaction that you do. However, we're all different of course, so if you find 'shooting up' (teeheet!) cold Copaxone is best, go for it!

I manually inject, and it's just always the way I've done it. I'm in such a habit of doing it now, it's second nature.

The SS nurse convinced me to do my first injection manually in the stomach, and I never changed from that.

I pinch 2 inches of skin in the area I'm going to inject (cept for the arms/behind, where pinching just doesn't happen the same) and wait a good minute + so the spot's numb, and then just go for it.