If you have rooted your Nook you can install Firefox mobile via the non-market link download link. However you will need to keep it up to date yourself as the Android market is used normally.

The Nook Tablet should really be named Nook Color 2. How difficult is rooting?

Rooting your Nook voids the warranty and if something goes wrong with it, then youre screwed. That is specificallya stated on the BN.com page and by calling them, they will tell you the same, so ROOT AT YOUR OWN RISK.''''''''bold text''''''''