I usually do it in the spring. There's no particular reason why-it's just that if I'm going to have to get the mower lifted up to pull the blade for its spring sharpening, I figure I might as well turn the thing all the way over and dump the oil out while I'm at it.
To be honest, I'd guess 90%+ of push mowers never have their oil changed(and B&S even advertises liftetime oil in their current engines as others have mentioned) so changing it at any point in the year puts you ahead of most of them out there.
I've "regressed" to 2-stroke Lawn Boys so don't have to worry about them at all now. With that said, I was getting ready to sell the Murray-branded B&S "never change" my wife bought new in 2018 and noticed that there were some pinholes of rust in the deck. Before I came along and started using it, I don't know what type of care it got, but I've certainly not abused it. It's also a $200 mower, but still the engine is still going strong while I'll go out on a limb and say that the rest of it is basically EOL.