12 gauge at close range will cut that snare wire..

You're welcome..

There's none made that are packable that I know of. Just a good set of side cutters and don't be greedy and try and cut it all at once, a third of the wire at a time.

I could definetly see the odd coyote snare being a danger to bird dogs.

If your going in the bush with your dog you should also learn how to loosen a snare.  It's not as easy as you'd think.  It takes someone to show you and a bit of practice. 

I say this because if the snare is tight, you might not be able to get the cable cutters on the snare without tearing your dog apart.  But if you know how to pinch them open it will make it much easy.

I should also add, when a domestic dog gets caught in a snare, most often they just sit there. They don't fight the snare. Snares aren't as dangerous to most dogs as people want you to believe.

Don't get me wrong, trapper's are ultimately responsible to take their snares down.  But with the new extended bird seasons there will be more dogs and snare problems. 

Another thing you should do if you bring dog's into the bush is know if your on a RFMA or not.  If you are, you should keep your dog close.  RFMA's will most likely have conibear's out for fisher, marten etc..  There's nothing you can do for your dog if they stick their head in a conibear.  But if you know your on a RFMA they are easy to avoid.

Jimmy I know those power snares scare the bejeeesus out of me !
 Areas like the EID and some big pasture land the amount of garbage
Laying around is really unbelievable. Concrete with rebar sticking out in the
  Tall grass is deadly , there are miles of old barb wire laying around .
  These are not wilderness areas ,quite populated , it's a crap shoot .
   As has been said , with the extended upland seasons ( which make no sense )
    That Birddogin and Dog snaring issue hasn't come to a head yet ....?