Half-Life: Alyx is a damn good shooter as far as VR goes, so it's no surprise that one of the earliest mods for the game adds a horde mode. It comes in the form of XenThug, which is available to download now.
Created by modder Manello, it operates like a fairly typical horde mode: waves of enemies approach you, and you shoot them. Every fallen enemy drops a bit of currency, which you can spend between rounds on getting kitted up. According to the FAQ, the mod will throw a bunch of waves at you featuring different enemy types, but once these are passed it'll cycle back to the beginning... only enemies will have double HP.
Manello writes that it's very easy to implement the mod to other user-created maps, so if XenThug proves popular, expect an influx of maps designed for it. Instructions for how to download and install are over here, and it's pretty simple.
The Half-Life: Alyx mods are slowly trickling in: earlier this week, a mod was released to enable non-VR play.
Cheers, Rock Paper Shotgun.