[2021] Why does Cold Conduction work with Totems?

Widely known mechanic that doesn't work on totems:

40% more Elemental Damage if you've dealt a Crit in the past 8 seconds

The damage bonus from that stat does apply to your totems, because they are using your skills. But a totem dealing a critical strike is not you dealing a critical strike, so them critting cannot "turn on" that damage bonus.

Cold Conduction

"your Hits" means any hits from your skills or your character's stats in the rare case of non-skill hits. Totems use your skills, hits with those skills are your hits.

Blast-Freeze also works with totems

This one is indeed a little less clear. The problem here is we have to balance accuracy for all cases against how over-complicated a stat description looks when the extra details don't matter for normal cases, which makes people confused about the simple application in regular cases. This is referring to freezes inflicted by your skills, or by you without a skill involved, which if spelled out in full in the description would make it too long and make some players confused about the straightforward non-totem case. These descriptions are ones I have notes on to try to improve in future.

In general, /u/taggedjc is correct.

They don't have any socketed skills to trigger. They only have one of your skills - the one they hit with.