Great isn't it? You wait for snow, and when it arrives it's the wrong type!
There's that old myth about eskimos having X (pick a large number) names for different types of snow, but if you are observant you certainly can see many different breeds of the stuff. Your problem is mostly one of temperature - at around 0 degrees C the snow is often wettish, but go down to -5 or less and it's just dry powder.
Mountaineers are quite well-versed in the varieties (if they have any sense, anyway) because avalanches often result from bad combinations of snow falling in layers. Steep slopes clear quickly, but shallower slopes can build up very dangerous strata of slab, powder and ice. If the snow can sit for long enough, it will normally start to consolidate into a large sheet of ice called neve (there are acute accents somewhere, but I'm going to leave it anglicised). Neve is partly the result of freeze-thaw action, but is also caused by crystal re-formation. Sublimation, condensation and sunshine all add to the mix.
You don't have to go to the mountains to see all this at work - my own back garden has been quite a good snow lab for 3 of the last 4 weeks. It's getting a bit boring now. It's occurred to me that people in countries where snow falls every winter probably don't bother much with snowballs or snowmen!