I guess it’s important to first understand the definition of freezing which is 0 °C (32 °F). Anything ABOVE freezing is generally liquid. Anything BELOW freezing is generally snow or ice.
Most hard-shells are not insulated, so they don’t exactly keep you “warmer” they just keep the wind and wetness out. The layers underneath the hard-shell will keep you warm. One can wear a hard-shell in many cases; they are just particularly good ABOVE freezing where more water is present.
Most soft shells have some insulation and are windproof. They are water resistant in a lot of cases, but not something you want to wear usually ABOVE freezing. One can also wear a soft shell ABOVE freezing, just so long as it’s not pouring rain, or your not rolling around in the snow all day.
I hope this is helpful.
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