My Lorenz manual calls for 30 weight. I put a funnel in a 1-gallon can, put a bedsheet rag over the funnel, and invert the just "emptied" oil jugs over the funnel whenever I change oil. I put those drainings in a pump oiler to lube the snowblower. The frequency of oiling is probably more important than the type of lube.
Tacky oils like some motorcycle oils, bar and chain oil, rock drill oil, to name a few, may adhere longer but also attract dust and grit. If you don't sand much for ice and snow, it shouldn't be an issue. Waxy, paraffin-like oils may not penetrate to the pins where lube is desired. On bicycle chains they are notorious for washing off in rain, and I would expect snow and ice would scour exposed snowblower chain.
