Most commercial ones I've seen and used have a constant thickness with the teeth on one edge.
If you're trying to go SUL, then I'd suggest you consider making a spine on the back of it for stiffness. That could be a bend in a single piece of thin sheet metal, hammered flat. Or a U-shaped channel J-B welded onto the main blade could serve as a stiffener. Titanium would be lightest (but most costly) and you'd need a way to carve the teeth.
But for UL ideas, see my thread on MYOG pull saws:
I really liked how that Plasti-Dip made the handle smoother and much easier to grip (less slippery). For larger objects, you can paint on the material instead of dipping it.
As a starting point, here's a commercial snowsaw:
$35, 35 cm blade length, 220 grams
But here are some custom bandsaw blades (carbon steel):
I suspect the 1" width and 0.035 gauge would cut snow nicely. It's thicker than what I used in my mini pullsaw (0.025) and wider, so it might not need any stiffening over a 12 to 15" length plus a 4" handle. But maybe it does. Done like a big version of my mini-pullsaw from bandsaw material at 15+4=19", it would come in at about 67 grams. Coated with Plasti-Dip about 75 grams. So that saves 2/3 of the weight of the commercial option.
On cost, the Plasti-Dip is almost nothing per use ($12 per can).
The 5-foot blade, 2 or 3 tpi, 1-inch width and 0.035 thickness is only $16.84. Less than $6 per snowsaw blade.