The drops would be Cryocitor (A pre-hardmode flamethrower type weapon that deals 12 ranged damage and uses snowballs as ammunition), Sub-One (a Spear shaped as an elongated Ice Key that deals 25 melee damage and has long reach), Kryosceptre (a staff that summons a mini-Kryonis that deals 18 damage and shoots projectiles), and the Frost Cubicus (an Ice Cube that deals 30 magic damage, but the projectile is affected by gravity and the weapon has a slow use time). In expert mode it would drop the Winter Support (an accessory that increase speed and causes the player to explode upon death, damaging enemies and buffing teammates).
Kryonis' Cave would be large but mainly horizontal. Only one spawns in each world, unless it's a large world, in which 2 will spawn. The boss is summoned by attacking it on it's head while it's sleeping on the ceiling (this is to prevent accidental awakenings). Summons and explosions will not harm it while it's sleeping. When it awakens, it will drop from the ceiling and fly up right above the player. It will begin to fire projectiles at the player while staying above the player no matter where he/she is in the cave (the boss will enrage if you leave from within 10 tiles of the cave). Then it will perform a spiral similar to duke fishrons and Betsy's and release a swarm of Ice Bats to harm the player. It will fly off and shake the cave to cause destructible ice stalactites to fall down. It will fly down and perform chain dashes similar to expert modr Eye of Cthulhu but slower. It will then summon a shield rendering it immune to projectiles and repeat the pattern. In expert mode, it will attempt to eat remaining bats after 16 seconds to regen health.
I wasn't aware of those rules. Thanks for reminding me! Also the boss enraging would keep the fight between player and boss, as external arenas (like floating platforms) would make the boss to easy. The only attack you would have to worry about is the ice bats, and they could fly off the screen and despawn preventing the bose from healing.