At Lvl 10 take whatever you prefer, though Summon Water Elemental is more effective with the Frostbolt build, as the splash attacks from said elemental are AoE and apply Chill, making your frostbolts easier and more potent.

At Lvl 16 take Snowstorm if you want to be able to clear and demolish the enemies, it's great if you took Ring of Frost and would then be mandatory. If you took Elemental and don't want poke, take Northern Exposure for your team to be able to burst, and if enemies are mobile and rely on that, take Numbing Blast.

At Lvl 20 upgrade ultimate, whichever you chose, and if you feel threatened by the enemy, or want to be able to execute, take Ice Blink, it's range will get you either to safety or within execute range, and the slow is a nice addition.

At Lvl 4 take Arcane Intellect if you're getting lower on mana, Frost Armor is great against a lot of melee though shouldn't be needed, for damage, take Frost Shards as it piercing will make it a lot more potent and dangerous.

At Lvl 10 take whichever ultimate you prefer, both are great, while Ring of Frost, will make your combos easier to land and your burst is slightly increased, take Summon Water Elemental if you want to be able to chase down enemies or escape, as it's not only another body for your team, it's ranged and it's attacks will Chill, aka provide slow and damage increase for your abilities.

At Lvl 16 take Northern Exposure for you and your team to be able to burst quickly, if you feel very confident landing your skillshots take Snowstorm, if you pair it with a teamm8's root, maybe your Lvl 10 if you took Ring of Frost, it will shred through the enemies.

At Lvl 20 upgrade ultimate, unless you feel threatened or want to be able to execute, take Ice Blink.