Does more snow mean there's no global warming?

No.  Of course not.  In fact, more snow is EXACTLY WHAT YOU WOULD PREDICT in response to global warming.  If you haven't seen, some politicians have been claiming that the recent "Snowpacalypse" (mostly in the Northeastern United States) disproves global warming.  Now, I know that it seems counter-intuitive, "How can there be so much snow if the earth is supposedly warming?"  Well, here's how:  Hopefully, we all remember learning about the water cycle in grade school.  Your science textbook probably had a figure that looked something like this:

Now, if you look at the right side of the picture above, you see that water enters the atmosphere by evaporating from large bodies like oceans... WHEN THE WATER IS WARMER MORE OF IT EVAPORATES and enters the atmosphere.  As you follow the arrows at the top of the figure, moving to the left, you see that all of that moisture in the atmosphere condenses when it hits cold air.  So you see, as global warming continues, we should see more precipitation (including snow) because the oceans will continue to get warmer and more water will evaporate and fill the air with moisture that, when it condenses will fall to the ground as either snow, sleet, or rain.  In fact, it is exactly because surface temperatures in the Pacific Ocean are warmer that we got so much snow (see figure to the right).  Of course, this warming is because of El Nino, not so much because of Global Warming, but it illustrates the point perfectly... WARMER WATER = MORE SNOW.