Southern New Mexico and Waterfowl Q's

[krink]

Before this get the ban hammer, yes this is about trad hunting.

Recently I found out that there is a snow goose season in February.  I am a pretty big waterfowl hunter (guns) but hearing about this season perked my ears for a possible trad hunt.  I have researched hunting there with not much success.

My very first worry is can I even hunt waterfowl with a bow there?  This is a big factor if I go or not and plus I dont want to get arrested.  Also where can I go?  From what I have seen in AZ as long as the land is not marked no hunting or trespassing you are fine to go on that land.  Is New Mexico the same?  

LAstly and most imprtantly is do you all have any tips on shooting birds on the fly?  

Thanks in advance.
Kyle