Does snow melt on ice?
Yes, a layer of snow on top of ice can melt in some circumstances. For example, one active area of climate research involves analyzing the optical properties of sea ice as they relate to incoming solar radiation. In some studies (e.g., Ehn et al. 2004) this involves snow layered on top of ice, with the snow explicitly melting (and later refreezing) over the diurnal heating cycle in some cases.

As a more specific recent illustration, this phenomenon was also reported for the Canadian Lowell Glacier in July 2018 by NASA. Abnormally warm air temperatures (up to 29°C/84°F, according to nearby surface observations) over several days resulted in the melting of surface snow while the deeper ice below remained intact - a process referred to as ablation.