expression, noun which may take the genitive case particle 'no'
mixed with snow
Describes precipitation or weather where snow is mixed with rain, sleet, or other elements. Often used attributively with の.
今夜は雪混じりの雨が降るでしょう。
Tonight, rain mixed with snow will fall.
雪混じりの風が冷たくて、外に出るのがつらい。
The wind mixed with snow is so cold that it's hard to go outside.
みぞれ specifically refers to sleet (a mix of rain and snow), while 雪混じり is a broader expression meaning 'mixed with snow' and can describe rain, wind, or other things containing snow.
Compound of 雪 (ゆき, 'snow') and 混じり (まじり, 'mixing'), the continuative form of 混じる (まじる, 'to be mixed').