Can I make the player freeze without powdered snow?

I want to give players the effect where snowflakes appear on the side of the screen, their hearts turn blue, and they take constant damage. Any idea how I can do this while the player is outside of powdered snow?

I tried /effect but that didn't work so I checked the NBT data of the player and of a cow using /data, and it seems that the tag that is changed while an entity is in powdered snow are Ticks Frozen. Setting this value to its natural max, 140, repeatedly on a command block did not cause the cow to take damage, and cannot be tested on players due to the way NBT data modification works.

currently, this is not possible...

...because freezing is not yet (if it will be at all, think the same thing with being on fire) a Status Effect.

...and it likely will not be possible in the near future...

...provided they decide to keep it that way.

currently, and as it may very well be in the future, the only way to give something freezing, as you pointed out, is by modifying the TicksFrozen data tag of an entity. because you can't modify player NBT data without the world being closed and via an external editor, it is not possible to make a player freeze in-game as it stands.