If you run a multi-grade oil in a lawnmower engine, all you have to do is watch the oil level a little more closely. Multi-grads shear down, and then slip past the rings. I always used SAE-30 in my 25 year old lawnmower engine (3 hp B&S), and never encountered much oil usage. On the last (annual) oil change, I put 10W-40 in, and it puffs a little smoke each time I rev the motor from idle to running speed.
Unlike a pump-fed car's lubrication system, small lawnmower engines are lubricated by splashing oil with a dipper connected to the crankshaft. Consequently, it doesn't hurt to run SAE-30 or SAE-40 oil, even in cold temperatures. That oil's getting slung around in there regardless of the viscosity. Only thing it'll suffer from while cold is some power loss due to the higher friction of the thicker oil.
Regards, Gary in Sandy Eggo