This is how you build a snowman when it's -30 all the time and the snow is too dry to stick together:
Wait until it's -18. The snow won't get any wetter, but when I lived in Calgary, I thought -20 was cold. Turns out you can still bundle up hard and go outside in -20 IF YOU HAVE TO. But in -30, with a -50 windchill, you don't even want to walk to your car.
Grab three bowls of varying size and a bunch of water conveyances. Fill your largest bowl with snow.
Pat it down.
Squirt water onto the snow.
Use, seriously, so much water. Use all the water you have for the bottom ball, and then go back inside and get more water, which you didn't want to do because this is already taking a while and -18 is still pretty cold. Add more snow, squirt more water until bowl stays full when you squirt it. Unbowl the bowl full of snow-ice (you have to take your mittens off to do this, mittens which are now kind of sodden-frozen because you've been packing down wet snow with them but it's still -18). Unbowl it where you want your snowman to be, preferably where you can see him from inside the house. Stamp down the snow around him, because your biggest bowl is probably Not Big, and the snow is super deep by now, and you don't want him lost in it.
Repeat with the next two bowls, and then burrow a hole into your Iceman's face and stick a carrot in.
You are not going to get any sort of coal or buttons or rocks to stick into the Iceman's face or torso, so he's just going to have to look like this. Good job.
And here's the thing with children, because I was totally like UGH NOT WORTH IT after all that. Eleanor kept falling in the snow (which was hip-deep on her) and not being able to get up, and both our mittens were wet and hers don't stay on and there were tears and I kind of just did the last bit really quickly because let's just get this snowman up and get back inside. But Eleanor is constantly at that window, all like Lookit! DERE he is.
See, Baby? Das our snowman. He have a carrot.
Now he has about a 2-inch snow hat, which Eleanor thinks is just a larf. She's forgotten about the wet mittens and the crying and how Basically Not Fun the experience mostly was, and she's just stoked on this little person we made out of snow.