Not sure if by fire but I assume it was an old wagon trail days term which referred to how fast it took to get to Santa fe using that area rather than through the pojoaque route to Santa fe before there even was a highway. But to be honest I don't think it's because of a forest fire or that sort of reference.
Burn trail? Is that the trail near Bandelier? If so, it would not have been named for the Cerro Grande fire. That trail was there years before before that fire. There's a trail near Bandelier called "Burnt Mesa" not sure what fire its named for. Cerro Grande fire was named after Cerro Grande peak I'm pretty sure. That's a beautiful hike by the way
Cerro Grande Fire
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