Of course no individual event is "proof of global warming", but this is entirely consistent with it.
This points out the huge failure in communication about climate change, but this is in fact exactly the sort of thing you would expect (and why "global warming" is such an easy term to misunderstand).
Short story is there is more energy in the atmosphere (i.e. heat) and it has to go somewhere. One of the places it goes is into higher variability in weather patterns, more energetic storms, changes is stable weather patterns. So that absolutely includes lower winter lows, as well as higher summer highs. Most of the modelling shows events like this winter storm growing in both intensity and frequency.
So far from the contradiction you (seem to?) see, it's pretty much what is expected.
But one might just as easily say that this event is entirely consistent with "proof of no global warming" also.
I woke up to a snow on Feb 15 is "just" weather. If I live in Austin, it was pretty weird. If I live in Anchorage, pretty normal. The difference between those two statements is not about weather, but about climate.
One lesson of climate change is that our past experiences of weather in a place are often going to become poorer and poorer predictors of next months weather. The fact that change involves a global warming phenomena tells us that both the weather and the changes in it are likely to get more intense.
I laugh at both color-teams, and heartily encourage Texas and any other states who so choose to secede, but it's still difficult for me to imagine that a giant continent-wide blizzard is a sign of global warming. How much deeper would the snow have to be, and how much further below zero would the temperature have to be, before we could call it "weather" rather than "proof of global warming"? In general I think "intense weather" is supposed to signify hurricanes.