Here's my two cents.
Yes, the storm two days ago featured sleet falling at 13 degrees due to the warm nose at ~750-800mb. Snow formed high up in the atmosphere and fell out of it, but when those falling snowflakes ran into that warm nose, they melted and turned into raindrops. After they exited that warm nose, they eventually refroze into sleet pellets.
I'm actually not entirely sure how a snowflake forms, but what I do know is that snowfall efficiency is determined by two things: temperature (amount of cold) and lift (which brings in the moisture and determines where snow grows). These two things are linked. Moist air is lifted high up into the atmosphere, and the cold temperature allows moist air to grow onto ice crystals (I think this is called deposition?). We don't want too little cold air where the lift sets up (-5 to -10°C) where snow forms because everything about snow growth is generally slower. The moist air doesn't grow onto the ice crystals quickly enough to turn into snowflakes. This causes a domino effect: ice crystal growth is slower so the "snowflakes" don't have time to really grow before they fall out of the snow growth zone, which also makes it harder for them to stick together, and what you see is usually more needle like. No dendrites. We also don't want too much cold air where the lift sets up (-20 to -25°C) because that'll mean there won't be enough moisture to grow snowflakes efficiently, so you'll see pixie dust. If, however, if lift sets up at the DGZ (-12 to -18°C), for some reason ice crystal formation is quickest (I have no idea why). This leads to bigger snowflakes in a shorter amount of time, which induces dendritic growth, or where snowflakes start clinging together. That's why you see those baseball sized beauties fall from the sky.
So generally, where lift sets up is where the snow growth zone sets up. Where lift sets up is where the temperature matters most for snow growth. Afterwards, temps below the snow growth zone shouldn't matter much unless it's above freezing (then we might talk about sleet/freezing rain). Hoped this helps. And if I'm wrong anywhere, let me know!