This is a concern in June, but generally no once we get to July. Check out the graph below taken from opensnow.com which gets it from NRCS. While we are actually expecting more snow in the mountains next week, what you can see is that we are getting ready for our big melt to start. There were some interesting stories this week about the snowpack "ripening". This refers to a time when there is melting, but the snowpack can still "sponge" up the water. Once it get saturated and we are warm (usually mid-May) the melt can be pretty steep. Of course I think if you went up at the end of June or beginning of July there might still be snow near the top of the passes, and I think you will be able to find snow pockets even when we are up there at the end of July. But by the end of July for HIH9 I would think it extremely unlikely that snow is causing passes to be impassible.
View attachment 1979221