In notes written around 1959, Tolkien experimented with various roots for impersonal “snow” verbs, first giving the aorist form of a derived verb Q. hrisya “it snows” < hriþya from the root √SRITH, then the present tense form of a basic verb Q. hríza “it is snowing” from the root √SRIS (PE17/168).

Neo-Quenya: The basic verb form †hriz- is likely archaic, since z usually became r in Quenya’s phonetic development. In this case, though, I suspect the medial z dissimilated back to s after the hr, since Quenya disliked repeated r’s (PE19/73-74). This occurred, for example, with the verb ras- “stick out” < †raz- < √RAS.

Thus, I would use modern Quenya hrise “[it] snows”, hrinse “[it] snowed”, ihrísie “[it] has snowed”. Since this is an impersonal verb, no explicit subject is required.