So weird thing I found out, Sentinels that freeze with Cold not only doesn't proc Arcane Ice Storm, but they also prevent you from triggering it if you happen to have another way to freeze the enemies.

[Rexis12]

https://packaged-media.redd.it/21j2sdzipx8d1/pb/m2-res_480p.mp4?m=DASHPlaylist.mpd&v=1&e=1719432000&s=862c1e33027db917807c8ca00907396d37cdca4d#t=0

As you can see, the enemies frozen do not proc Arcane Ice Storm, and using Avalance does not override it.

[Void2258]

Griefing Arcane Ice Storm is a thing since ANYTHING (sentinel, other warframes, etc.) can block it going off. Unlike any other arcane in the entire game.