IMHO the expression "cotton kills" comes from mountain rescue teams etc who rescue persons clad most unsuitably in cotton jeans and t shirts etc.
Such clothing is of course suitable only for fine weather.

Cotton clothing of reputable manufacture, designed for cold conditions, such as the ventile garments refered to above is quite suitable.

Cotton long underwear looses its insulating properties if wet, it is therefore totally unsuitable (and may well kill) if the wearer gets wet. Wool or synthetic fibres would be much more suitable.

Cotton long underwear (tops and bottoms) is very suitable for cold dry conditions, such as in unheated homes , vehicles or workplaces, or in case of fuel shortage, failure of heating plant etc. I would also wear cotton long underwear for outdoor work or gardening etc were there is little chance of geeting wet.
Cotton is moderatly priced, can be hot washed or even boiled without damage, and is far more comfortable to wear than wool or synthetics.
Such articles dont seem to be sold in the UK, I had to purchase from the USA.
Here in England it does not often get cold enough for long underwear to be required, though I consider it prudent to keep a good supply just in case.