In the game Yuki is the worst logia; this is an opinion shared by a lot of people. It has the least moves, no damage, no utility other than logia reflex, and in general just sucks. It can be cracked with certain move combinations but its not fun even when used in ideal circumstances, relying on only one trap and then spam to easily win.
Much like Suna, these new Yuki moves will work by default and be empowered in snow biomes/when its already snowing. In other cases, these moves will be dependent on a reworked yuki snowstorm move, much like how suna must use ground death before quicksand.

Reworked snow storm: Much wider AOE (comparable to ice age, maybe larger since its no damage or CC), minimal frostbite applied on use, but the falling snow continues to fall for quite some time (maybe a very long active move that can be canceled like zushi flight). Over time frostbite can build up if you stay inside the storm for too long.

Snow surface teleporting: An instant teleport move that can be only used on connected snow surfaces or blocks. No beam like goro or pika, or at least for a much shorter time and not visible to other players, but a longer actual teleport time. Ideally just snowflake particle effect for like 2 seconds for the actual teleport. If hard can just be instant like goro and pika.

Invisible flight through falling snow: Only usable while snow is falling from either the snowstorm ability or snowy minecraft weather, its logia flight, but unlike normal logia flight, the entire body is replaced by snow particles, making it very difficult to discern the position of the flier amidst the falling snow. Almost as fast as gasu, but cant attack except through using snow abilities or mannen yuki. Observation haki AURA in this case would ideally show blue highlighted snow particles rather than a body, or not work at all. Not sure if there is any confirmed cause of kenbunshoku haki allowing a user to sense a fully morphed logia in the aura sense. Obviously future sight would still work to detect attacks.

Mannen Yuki: An attack that differs depending on how its used. Normally a melee grapple ability like suplex that deals significant damage and applies many stacks of frostbite, but if used while in snow flight, can be used at range and will teleport the user to the target before doing the same move. Applies at least 5, maybe 6 or 7 stacks of frostbite instantly, blurring the targets vision with snow and cold. Suplex level cooldown, longer if used in the teleport form, but maybe shorter if it kills the opponent, to give yuki some sort of rapid npc kill grinding utility which it lacks. Visually can just be a swirl of snow particles around the opponent while freezing them in place, nothing fancy. Bypasses logia, but magu and mera are immune to the frostbite effect, from any attack.

Snow morph: Like sui sui but restricted to blocks with snow on them, or snow blocks. The ability to swim through the snow at a decently fast pace, simulating monets power to hide in her own snowstorm.

Cold touch: Inspired by how monet would simply surround people with herself as snow to freeze them, an ability similar to pika's light acceleration, but instead of a damage buff, it only makes your attacks apply frostbite on hit with ur hands and feet. For those who use brawler or leg instead of the sword. Lasts longer than light acceleration with a similarly short cooldown, as its no damage buff, only frostbite.

In addition the regular construction moves will be larger in snow biomes or inside yukis snowstorm ability, much like how suna is empowered in a desert. The inside of the globes will be larger, the double kamakura will get an extra layer, and the wall will be larger. Cooldowns will remain the same unlike suna to offset the fact that the buffs can be gained with the snowstorm move like a domain, unlike suna which can only create sand to use in other biomes and is only buffed in the appropriate biome.