We live in far northern Wisconsin - and have had a winter of over 120 inches of snow. Great time to get a puppy! Well fast forward to today.....the snow is rapidly disappearing. Our 6 month old female, Lola, has always (in her short lifetime) pee'd and pooped on snow. This is her preference, clearly. So now when we take her out, she holds her pee and poop until she finds a spot with some snow. We've tried to clean up around the house a bit, but she is not interested in doing her business unless she's on snow. I am guessing this will solve itself with time, but would welcome any suggestions.
I've seen it written a thousand times that dogs are not very good at generalising, but I think this has got to be my favorite example ever! Sorry, I haven't got anything to suggest (Jade's answer is reassuring!), but that is fascinating!
I've neve e experienced this myself as we live in Australia. I wonder if, next time she does a poo, you move it to a snow-free spot. Then when you take her out again, she might be more happy to poo where she finds another one of her poos. A friend did this with her dog when he would only poo in the back yard.