Most of the regular headlamps you can find are generally only weather resistant (ie. rated around IPX4). If you want one to survive regular immersion, you need to look for ones that were designed for uses like caving or diving - that is at least rated IPX7 or IPX8.
The ones that survive full submersion typically have screw in battery compartments as opposed to click in battery compartments like the Black Diamond Cosmo mentioned above. The BD Cosmo for example states "... If submerged, water may enter the battery compartment and it will still operate; it should be completely dried out after use in wet conditions." I've had a look inside the Cosmo battery compartment, and I am dubious about that claim - I think it should state it "may" still operate.
For decent waterproof headlamps for example, there is the Nitecore HC68 or the Fenix HM50R mentioned by Lamont which are both IPX68, and there are some Petzl headlamps like the Duo series which is IPX7 rated.
These can be quite bulky and heavier than the typical bushwalking/running headlamps though. I had a Petzl headlamp die on me while caving so I don't buy Petzls anymore.
I carry a few single AA/14500 torches as backups - both mine have survived regular submersion. I like these type of lights as I have a lot of rechargeable AAs and 14500s around. I use a head strap like the
https://www.fenixlighting.com/product/headband/ https://www.myfenix.co.uk/product/fenix ... dband-1542 or the
https://flashlight.nitecore.com/product/hb02 if I need to use it on my head.
One of the smaller headbands I actually use as an arm holder instead, and if walking for longer durations in the dark I will use it on my arm instead of on my head.
For activities with more water involved - like kayaking or snorkeling, I will carry a small Divepro Pygmy diving torch, which also accepts AA and 14500 cells.