It always interests me to see how other people envision each of the characters in a book series. This is what I picture them as, some of them because their picture is on a cover, giving it away but others are just imagination:
Alpha (Sweet) - Greyhound
Beta (Lucky) - Golden Retriever/Sheltie mix
Twitch - Irish Setter mix.
Snap - Beagle mix.
Bruno - Chow Chow/German Shepherd mix.
Bella - Golden Retriever/Sheltie mix.
Mickey - Border Collie.
Storm - Doberman.
Arrow - Doberman.
Woody - English Labrador.
Moon - Border Collie.
Dart - Whippet.
Daisy - Westie/Jack Russell mix.
Rake - Irish Wolfhound.
Breeze - Chocolare Lab.
Chase - Small, shaggy mutt.
Beetle - Mastiff/Border Collie, sort of like a Newfoundland in appearance.
Thorn - Mastiff/Border Collie, more like a Collie in appearance.
Ruff - Sort of like a shorter-legged Patterdale Terrier.
Omega (Sunshine) - Maltese.
Fiery - Mastiff
Terror - Pit Bull
Martha - Newfoundland
Whine - Pug
Whisper - Blue Heeler
Old Hunter - Bracco Italiano
That's about it. There were some other, more minor characters, but I didn't feel the need to point them out.