As u/delejahan pointed out, the most plausible botanical identification is ephedra. This was almost certainly the case in the recent past, as European observers in Yazd recognized the plant that the local Zoroastrians called "huma" and used in some ceremonies. That would also fit with Avestan descriptions of haoma being wither white or gold, reflecting different ephedra species in and around Central Asia.

As for intoxicating effects, it would depend quite a lot on the actual variety of ephedra and season when it was harvested. Some species have relatively high concentrations of ephedrine during their life cycle, a relatively minor stimulant by today's standards but comparatively powerful in ancient times when casual stimulants like caffeine or nicotine were not common or available at all. Other species have barely any ephedrine at all, and the visual differences are often minimal.