Keep in mind that your feet are also smaller earlier in the day, so depending on when you tried on the boots that might affect it.
I know nothing about ice climbing, but fwiw, my mountaineering boots are a 39.5 and fit perfectly. I typically wear a size 7.5-8 shoe with normal thickness socks. I recently picked up a pair of Mont Blancs that fit me almost exactly the same way, in a size 39.5. I realize that shoes fit everyone differently, but I also have trouble believing that you'd be happy with a full 2.5 (European) sizes smaller than me if you're only .5 to 1 full size smaller. Another one of my friends with the Mont Blanc is very happy with them in a 37, and she's typically a size 6.
If I were spending a bunch of money on boots, I'd want to make sure they fit really well. I would at least try on the 37.5 before deciding to keep the 37. I'd also try on some other brands, since Scarpa tends to run wide and it sounds like those boots may not be an ideal fit. If your toes are hitting the end, it's pretty clear that the 37s are too small for hiking.