A verb in the Quendi and Eldar essay from 1959-60 glossed “be chill, cold (of weather)” (WJ/417). It also appeared in some etymological notes from around 1959 as a derivative of the root √NIK(W) and with the glosses “to snow, it is chill, it freezes” (PE17/168). In this 1959 note Tolkien gave several inflected forms making it clear nicu- was an impersonal verb: nīqua “it is freezing”, nicune “it snowed, froze”.
Neo-Quenya: For purposes of Neo-Quenya, I’d mostly use nicu- as an impersonal verb for cold weather: nique “it is cold, it is freezing”. For the freezing of water or similar substances, I’d use ᴺQ. hel-. For “to snow” I’d use ᴺQ. hris-, a modernization of archaic †hriz-.
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 verbs, no explicit subject is required.