Anthropogenic: "there's more snow falling in Antarctica than ice melting" says nothing about humans being responsible one way or the other.
Global: more snow falling in Antarctica says nothing about overall global conditions, e.g. average surface temperature. Changes in circulation patterns can cool one spot and warm another.
Warming: more snow falling in Antarctica does not, by itself, even say anything about temperatures in Antarctica. It's not like raising the average there (-49C) by a few degrees would turn snow into rain. It could however increase the likelihood of precipitation.