The order of operation usually goes something like this.

1) build mask (a multi-stage process I won't go into here... it's a fair bit of work)
2)cut veg-tan structural panels (front panel and back/flap).
3)dye interior facing (the finished side of the veg tan) - if needed.
4) attach mask to flap, along with the chrome tanned back cover. Add strap keeper now.
5) attach fur to front panel.
6) attach gusset to front panel (then 'roll' it make the self-welt)
7) attach back-edge of gusset to rear panel, then add trim to cover the 'joined' edge.

The gusset can be a thin chrome tan, or fur. In my experience, unless you're a genius working with both fur and leather, you're better off using chrome tanned. Otherwise the fur will bulk out and the over-all bag will be VERY shaggy. Fur can be a PITA. It gets into your stitching, is messy to cut, and bushes out in wild, sometimes unexpected ways. But when done right, it is really 'pet-able'

With certain furs you can 'shear' them down to a workable thickness, but it's probably more trouble than it's worth.

Again, I'm no 'full mask' expert. I've just worked with enough fur to know how irritating it can be