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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.