Ok, I'll write what I know first then go to narutowikia to get additional info if there's any info left..
Ice release was the first KG to be ever shown in the whole it was only used by Haku in the manga however there was some ninja from Yukigakure that can use ice release too, they appeared in the movie that I didn't watch. Ice chakra is formed when the user adjusts water chakra using wind chakra to cool it down under the freezing point. it can be used to either freeze a pre-existing water source or make ice out of thin air. Being simply frozen water, ice is strong against fire and rain (I think) and weak against scorch, earth, steel, and storm (I think)..
that's all I could remember now.. gotta check the wikia and the weakness/strengths thread and edit this post
Thats ok no need to edit, the only thing you forgot is lighting is strong to Ice aswell. I like to think of ice as a more useful version of earth as they share alot of similarities. Both are weak to lighting and strong to water, both can block a fire jutsu of equal rank and both are solids that can be used to manipulate the terrain. Main difference though is for most earth jutsu you need contact with the ground for ice however you can use it in mid air and create it out of thin air unlike earth. Now then onto the training.
Vegito is in the middle of doing one armed push ups counting outloud to himself: "100..." as Vegito see's the young girl approaching him he counts louder "2 trillion!, oh I didn't see you there!"
Vegito jumps up to his feet and taking a good look at the girl he realizes almost right away.
"You're also a Yuki I take it? But you're still a newbie. Then its a good thing you came to vegitos training camp, I'll show you why our kekki genkai is the best one out there!"
Vegito takes the girl to a frozen tundra.
"You're shaking right now but when I'm done with you, no cold tempature out there will be able to affect you!"
Vegito sits down and breathes slowly.
"Meditate like this, feel the cold air, the snow, the atmosphere. Do so until you no longer shiver become like ice."
Vegito stands up and walks away
" You must survive here in this cold for a month then I'll return!"
vegito leaves Resha to her own devices.
So describe your month in the tundra and how you learn to adapt to the cold