Most sources on the internet agree that Anahita's four white horses are named Wind, Clouds, Rain, and Sleet. These are obviously the English translations of these words. I am looking for the original Avestan words. As far as my research has gone, I have found these as the originals: Vayu “wind”, Maēγa “clouds”, Vāra “rain”, and Snéshar “sleet” Since I do not know Avestan, I am uncertain how correct these are. Any help with confirming or rejecting any of these would be greatly appreciated.
(Just for what little it worths, "most sources on the internet" seem to be carbon copies of each other, be it Wikipedia, Encyclopedia Iranica which seem to refer back to articles in JSTOR. Anyway.)
A search through An Avesta Grammar in Comparison with Sanskrit reveals that you're on the right path with early Iranian roots:
WIND --- Av. văyu-, Skt. vāyu-
CLOUD --- Av. maēʒəm, Skt. mēghám
RAIN --- Av. vāra-
SLEET --- Av. fyawhunte (they shower sleet)
The Avestan text the four horses of Anahita can be found in and its English translation is here, p 201. I am not convinced these are names per se. It seems that the supposed names are simply describing the four horses: āsyangha vātaēibya, swifter than winds; āsyangha vāraēibya, swifter than rains, āsyangha maēghaēibya, swifter than clouds. Throughout the text, the editors seem pretty consistent when capitalising names.
Sraoshem1 ashīm2 huraodhem3 verethrājanem4 frādat-gaēthem5 ashavanem6 ashahe7 ratūm8 yazamaide9. Yim10 chathwārō 11 aurvantō 12 aurusha13 raokhshna14, fraderesra15, spenta16 vīdhvāonghō17, asaya18 mainivasanghō 19 vazenti20 sravaēna21 aeshām22 safāonghō23 zaranya24 paiti25 thwarshtāonghō 26. (28) Āsyangha27 aspaēibya28, āsyangha29 vātaēibya30, āsyangha31 vāraēibya32 āsyangha33 maēghaēibya34 āsyangha35 vayaēibya36, hvapataretaēibya37, āsyangha38 hvastayāo39 ainghimanayāo40, (29) Yōi 41 vīspe42 te43 apayeinti44 yōi45 ave46 paskāt47 vyeinti48, nōit49 ave50 paskāt51 āfente52. Yōi53 vaēibya54 snaithizibya55 frāyatayeinti56 vazemna57 yim58 vohūm59 Sraoshem60 ashīm61. Yatchit62 ushastarire63 hindvō 64 āgēurvayeite65 yatchit66 daoshataire67 nighne6
We worship1 the righteous2 and the holy6 Srosh Yazata the beautiful3, victorious4, bringing-prosperity to the world5 and Lord8 of righteousness7. Whom10 four11 white13 steeds12 (abi)brilliant14, beautiful15, divine16, wise17 (and) (abj)shadowless18 carry in the wagon20 in the (abk)heavenly spaces19. The hoofs23 of those (horses) are laden21 and gilt26 with gold24. (28) They are swifter27 than (other) horses28, swifter29 than winds30, rains32, clouds34, birds36 well-winged37 (and) swifter38 than arrows40 well-aimed39. (29) They (horses) (abl)can overtake44 all42 those43 who go in pursuit of them. The pursuers can never49 overtake52 those (horses). Who53 (horses) speed on56 (while) carrying57 in the chariot57 the good59 holy61 (Sraosha yazata) (when he) takes his course65 in the eastern-most63 Hind64 and abmalights down68 in the West67, (i.e. starting from the Keshvar-region called Savahi he goes to the Keshvar-region called Arezahi.).
abh For its translation see 1st karda of Sraosha yasht Hādokht.
abi The meaning of “aurusha” is also “crimson”. See Tir yashta, 1st Kardāh.
abj i.e. (Steeds) who do not cast any shadow; a=not; saya=Persian sāyeh=shadow. Dr. Mills taking the word as “āsava” translates it as “swift”.
abk Or moving in accord with the divine will (mainyava + vasangha)
abl i.e. the speed of the horses of the holy Sraosha yazata as mentioned in this paragraph is swifter then wind, bird, arrow, etc