When it's warmer, they have nice lined gloves too and both the mitts and gloves come with packets of wax to apply to them and that really does help keep them dry and last longer.
Your first product is OK but the gauntlet is just too short.
1st url below not too bad.
2nd url below is better.
Something like the 2nd one - - - they take that acrylic liner and pitch the thing - - - - get an avid knitter to make you some comparables except out of wool .
Cheap - - - nope - - - - but you will not have cold hands unless you are wearing some kind of a cheap cheesey toque - - - - likely out of acrylic - - - - either double it up or even better get a wool one under a slightly looser acrylic one.
I've had opportunity to work for most of a 12 hour shift for more than a few days at a time when it was between -40 and -42 C.
Work shut down at -42 C but I did not suffer from cold hands nor feet nor head. Layers with air spaces - - - small - - - - in between.
If you buy a good pair of leather gauntlets you might get about 20 years or more of cold weather wearing out of them.
Liners - - - not so much but they can be darned and/or replaced.