Hungarian Historical Phonology nemez
nemëz 'Filz'
First attestation/Old Hungarian data
1395 nemes, nemeʒt (see EWUng 1023, s.v. nemez)
Important dialectal forms
[coming]
Uralic/Pre-Hungarian reconstruction
WOT: 1334: Ancient Hungarian *nämeδə < Ancient Hungarian *nämetə
Cognates suggested in earlier research
None
Loan etymology
Hu nemez ← Iranian WOT: 1334: Hu nemëz < Ancient Hungarian *nämeδə < Ancient Hungarian *nämetə ← Al *nämet
Commentary
The Iranian origin of nemez is transparent and is accepted by all the relevant sources. This is one of the loans preceding the change Hu z < *δ (< *t); it is unclear to which phase the word was borrowed: WOT (1334) assumes it was borrowed when Proto-Hungarian (WOT: "Ancient Hungarian") still had *t. WOT (1334) considers the word an Alanic loan, but it remains unclear why the word should be specifically Alanic loan, as the word is found in numerous Iranian languages.
WOT also mentions that the word is a "cultural wandering word", but in any case the immediate Iranian origin of the Hungarian word seems most likely.
Conclusion
A convincing Iranian etymology, borrowed before the latest phase of Proto-Hungarian.
References
EWUng 1023, s.v. nemez: Hu ← Iranian
WOT: 1334: Hu ← Alanic