I have read that snow falls at 32 degrees F. While at an altitude of nearly 8,000 feet above sea level, I found it snowing, but the temperature was more than 40 degrees F. Perhaps the indicator is broken, but the outside temperature did not seem cold. Does higher altitude, or thinner air, have some affect on what temperature it can snow?
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Snow can only form at, or below, the freezing point of water. It can form at any temperature below freezing. (Of course, freezing point is pressure dependent). Snow formation requires moisture in the air. Warmer air can hold more moisture. Snow flakes cool the air around them, allowing them to land on ground warmer than freezing point - they can then both cool the ground and insulate flakes landing above. In short: it can never be too cold to snow, but it can be too dry. - I think you can derive the answers to your questions from that.