Building a Cold Witch need advice on tree

Just like the title says. I'm trying to plan a build ahead of time for my witch and want advice on how I can improve my build. It's based on maximizing cold damage. I'm still new to the game.

https://www.pathofexile.com/passive-skill-tree/AAAABAMBAAFvBAcFQgW1DdEOSBBYEQ8RUBSwFdcXVBslHU8d2R8CIG4igST9KgsqWyycLL8tHzB8MjQ1uTbFN4FBlkM2Q1REq0V8RwZLrkwtTLNQMFFHUrJS7FPUVEdVrlZKVmNZvFxrXfJfKmNDZJ1tGXBSdFV4znn2ghCCHoRIhq6IQonTi3qMNo2Cjb-OPI-mj_qVBJeXm6GeoZ7EnwGkeKa-pyuus6-btDi0xbmTwUnBxcHVwuzDCcNtxSjI3NDQ0PXR5NMb2VvbAtte2-fe-N-K37Di9-NW44Tk6-UZ51TpAuvk6_XsGPId8uH0cfZb99f5yPv1_h3_3g==

The build will be a CoC Wand build using these gems so far.

Barrage
Critical Strikes Support
Cast on Crit
Pierce
Arctic Breath
Glacial Cascade

If you have any advice on the gems as well I would appreciate it.

If you want that to be your starting character in the new league i strongly recommend a life instead of a CI build. It will be difficult to get the right es gear on a first char.
Besides you will probably end up wearing a tabula rasa as you need the 6 link and as CI you can't afford to loose the potential ES from a chest.

Your tree ain't good for a coc build:
The damage from a coc build comes from proccing multiple spells as often as possible. Only if the proc speed is much higher than the cast speed when selfcasting, then the damage will be higher for a coc build.
That means your number one priority is to ramp up crit chance, accuracy (if not using a vagan dagger) and attack speed. Spell damage nodes are secondary. If you invest too much in the latter at the expense of the former your build won't work.

Wand isn't the best weapon choice.
A vagan dagger that never misses is much easier to aquire than an imbued wand with high crit and attack speed.
If you want to use a ranged attack, quill rain is a better choice. Easy to get, much cheaper than a wand, usable from low levels on and with the introduction of the shadow's assassin class able to have a high crit rate.

You should really reconsider starting as a witch. Shadow and the assassin ascendancy is a much much better choice for coc. There is a reason that there is a shitload of coc builds in the shadow builds list but not in the witch list.
I recommend looking at some quill rain coc builds in the shadow list (most use spark and ethereal knives though because of the projectile speed bonus from quill rain).

BTW if you still want a CI char you can use a Soul Strike quiver with a quill rain.

I've seen some builds on youtube for witches that look really good. I like the Shadow Assassin but casting spells looks more fun. I could do a spell casting Assassin I suppose. I'll post in the shadow forum to see if it would work.