Have a look at this document:

https://directives.sc.egov.usda.gov/OpenNonWebContent.aspx?content=17753.wba

I believe some of the experimental catchments and watershed studies, such as those at the Rocky Mountain Experiment Station (USFS) and areas where snow accumulates at higher elevations to also glaciers have examples where snow, rain, streamflow, temperature, solar radiation, forest cover and other factors have been evaluated. In many instances, streamflow melt is quite predictable, and bankfull flows may last for extended periods. You might look into End Member Analysis to see if there might be some chemistry means of separation such as described by Garrett et al and others. What is not so predictable is severe storms with warm rainfall on snow (rain on snow) as these can cause severe floods such as the 1964 flood in Oregon and N California. Snowpack insulates frozen semi saturated soils which may be unable to absorb rainfall, encouraging runoff in such events. Since most hydrologic studies do not try to separate out contributions related specifically to snow, it may take some gathering, compiling and sharing of data to direct results toward this end. But there are some individuals who related to their specific circumstances have some good ideas of when accumulated snow is actively melting and contributing to flow. Besides cover such as forests, aspect and slope can also be influencers. There are several snowmelt runoff models and research papers available, and contributions from many countries where these subjects affect hydrologic response.

Right way:

Simulate using some hydrological model. e.g., SRM, SWAT, SPHY.

Shortcut:

Multiply final runoff with the ratio (snowfall/total Precipitation), and then subtract from total runoff to get the runoff contributed by rainfall. (if these two are the only sources of total runoff)