Does cold damage counteract bleeding?

I’m doing my first play though of poe1 after playing a couple hundred hours of poe2 early access. Im playing as dualists/ gladiator. Duel wielding swords. My primary skills are Vaal double strike, lacerate, and splitting steel for when I need a range option. Currently in Act 8.

I have been focusing on dual wield passives, bleeding and evasion but I have started using herald of ice and hatred to buff my damage but I was wondering if all the bleed build up gets negated when enemies get frozen? I don’t seem to do very much bleed damage.

Thanks in advance