Grahame
I have one of these

- Half Face Mask.jpg (83.97 KiB) Viewed 11207 times
The wrap design is very similar to the Cold Avenger that Moondog posted. Probably a copy of that design.
I got it as I wanted something easy to put on with gloves, that also covered my ears and not too expensive. I also use a merino buff (I have various Icebreaker, Platypus and Macpac versions), that I usually double fold if it's really cold.
I've had mine for about 2 years or so, but they can be found from the various Chinese sellers as a "cycling mask" or from Amazon
https://www.amazon.com/dp/B00JWMV17I as this half face mask (Check the reviews there - it is funny to read the reviews of people getting this for Corona though since it's not designed for that at all). I paid less than $5 for mine.
The majority of the mask is a thin fleece material that comes down to cover the neck only at the front. At the back it doesn't cover the neck at all which I like as it doesn't get in the way of the collars of my tops/jackets. I've only used mine around -10°C maybe -15°C. Any colder I think a thicker fleece might be better. Around the nose and mouth it is a thin neoprene material with punch out holes. The "valve" is a furphy - only for looks. The holes in the neoprene and the nose triangle cutout does let out some condensation and the top design doesn't fog up my glasses as some other masks do. I have a fat head though, and the velcro only secures half way - the tight fit probably seals the top from fogging my glasses. I had meant to sew on an extension to it to make it a bit more comfortable, but never got around to it.
I haven't use it over 4000m, mostly from 2500-4000m. I've given up on my thoughts of trekking over 5000m after I struggled at 5500m. A mate asked if I wanted to join him going up Acongagua in December, but I had to decline. I think only a third of his group made it to the summit.