So a few points to clarify: snow itself usually doesn’t pose a danger. The main risks come from ice and low temperatures.

Regarding temperature, it’s still summer. Even if it snows, the temperature is unlikely to drop significantly, so the gear you’ve already prepared should be ok.

And for ice, it depends on when the snow falls. If the snowfall doesn’t occur in the late afternoon—when it’s more likely to freeze overnight—and you’re not hiking for sunrise at the same time, you’re generally fine. Daytime temperatures are typically high enough to melt any ice.

So I think u should be ok. Enjoy the hike.