No, it is not okay to use an oil not recommended by Honda. You use the snowblower in cold temperatures that is why Honda recommends a 5 weight oil. There's no reason whatsoever to use 10W-30 weight oil. Use 5W-30 as Honda recommends and nothing else. I also recommend you use a 100% synthetic oil in any air cooled engine.
Yes 10w30 is a good oil for snowblower or lawnmower.
SAE 10w30
SAE 10w30 synthetic oil.
SAE 10w30
As a snowblower is used in the winter use 10w30 weight synthetic oil and change the oil once each year.
I have a Honda GX 340 and the toll shop I bought filters and oil said it is 10W30
10w30
Honda ATF if Auto(don't use Dexron/Mercon) and 10w30 oil or Honda manual Trans fluid(which is fancy 10w30)
5W30 conventional oil. Straight out of the manual.
10w30
SAE 10w30
10W30 or 10W40 motorcycle oil is recommended by Honda.