That, I cannot properly answer. The animation could be something like them starting to slip, and they would be "stunned" during that time. That would be something short.
This tile is more so designed to punish fast units by causing them to slip/slide around. There are several fast units with a high Dexterity that would help prevent them from suffering a penalty, thus going against what the tile was inicially intended to do. So I think it should be kept to movement speed only for that very reason.
Besides, the Horned Reaper has a high Dexterity. With such a wreckless personality, do you think they'd think twice about walking carefully across ice? Also, Giants actually don't have that bad of a Dexterity stat. Bile Demons are the ones with an awful Dexterity Stat. It is so low, they'd probably slip more often then they should.