>>56043499Blizzard is 100% under Snow, regardless of which pokemon is using it.
All the things that you mentioned except for the last thing aren't inherently part of the Ice type but merely a move distribution issue.
Don't get me wrong, I believe there is value on using Ice type mons, but your argument is not the strongest.
>STAB>50% defense increase under Snow>Potential baiting to the opponent by begging them to attack you and either switch out or tera