That's exactly right. Air can hold an asston of water. But it decreases exponentially as you approach absolute zero. I think at around -20 or -30 you can hold something like .2 lb of water per x,000 cubic feet of air. That might not be a lot relative to water capacity at 100 degF, but it's still something. The biggest thing is that you also have strata of air pockets. Look at a
sounding diagram and you can see that the air above the ground can be warmer and more humid than the surface temperature. As the strata mix or exchange energy and water, snow can easily happen even if you're at a very low surface humidity.
More on soundings:
Link
ETA: This is why I have learned to really like advanced weather sites that go beyond "Here's our custom 'Feels Like' temperature that scales from 'It's a *** bit nipply' to 'Oh dear...'"
Shut up and give me the numbers. A good way to know a good site from a bad site is whether they give you humidity in relative humidity or dewpoint. If you get RH, find a new site.
There are also more advanced variables like CAPE, lifted index, CIN, and many more that can give you a far better idea of what's coming and the potential than "Looks like ran, Hal"