Snowclash CTC blizz stack with +skills?

[zeskelnec]

Charges do not get bonus from +skills items.

For Chance to Cast.
1) In general , does CTC get synergy and +skills bonus?.
2) In particular
Does CTC 16 Blizz on snowclash becomes lvl 23 with Occy + Viper + lidless and does it get % bonus from hard points in synergy skills ?
It looks logical at least that Cold Mastery enhances CTC blizz dmg.

[FrostBurn]

I'm almost certain that any CTC spells will be at the slvl stated on that item and +skills will have no effect on them. CM, of course, will lower the cold resistance of any monster and acts on its own, which is why it will help increase the damage of a CTC blizzard, AFTER it has been cast.

[zeskelnec]

What about synergies on CTC ? Does CTC blizz get % bonus from each hard pt in glacial spike ?
What is painful then, is the CTC valkyrie lvl 15 on Peace, coz it will not be spawned at lvl >= 17 with cruel pike or other good mod.