A few questions....

ORIGINAL: trinity
Secondly, the new boy seems fond of chasing the cat. He hasn't hurt her, and doesn't act aggressively, but I am wondering if there is a good way to deal with it.

 
Maybe you can teach him "leave it" for the chasing and, if your cat is okay with it, supervise whenever they play.

ORIGINAL: trinity
Last, this is a simular question, if the dog snaps or growls, what is the best way to deal with his action? Trinity has never been that snotty, but he gets very grumpy sometimes....

 
Depends on why he's growling. Growls aren't necessarily aggressive in nature nor are they bad. If you mean the aggressive kind, I would distance myself from the dog and maybe give him a command like "Sit" (something you are sure he knows very well and will follow). It really depends on why he's growling, though.

do you use plastic dishes? i have heard they can cause brittle hair and dry nose/eyes, im not sure why, but maybe the chemicals that can leach out of the plastic.
 
i don't know where you live, but winters where i am are very dry and if i don't run a humidifier it gets too dry and my dog's nose gets dry just like our own.
 
you should have a vet look at them though since you do not know the cause. it's normal for the nose to benot as wet sometimes, but not to be completly dry for long periods.

No, actually I am using some old camping dishes, and they are metal. Good to know about the plastic, though, because I am going to buy them some new dishes.

I have 5 fish tanks in my home, ranging from 75-5 gallons, and it's pretty small, so i doubt that humidity is a problem...

I just had both of them in the vet last week, (Trin the week before that) and they checked out ok, by the vet...

A dry nose by itself doesn't mean anything. Only if there were others symptoms of illness (loss of appetite, cough, etc.) or if it was severely dry to the point of being chapped and cracked should you worry about that.
 
When and why does your dog snap and growl?

It seems to happen when he is chillin' on the couch. If we go to cuddle him and he doesn't want cuddles, he will snap, or growl...

Could he possibly be resource guarding the couch or something that he has while on the couch??  Maybe just a wild guess but that was my first thought. 

Izzy chases one of my cats b/c she runs from her.  She runs from her b/c she chases her.  It is a vicious cycle and I don't know how to change it.  She and the other one actually play sometimes.  Neither of the cats run from Harley b/c he has never been one to chase them.  Not that this helps in any way but maybe it will give you some perspective?

He could be guarding his spot on the couch, but also bear in mind that dogs do not like to be hugged. Most will put up with it but some dogs won't... none like it. Petting and cuddling can be great, but the way humans sometimes approach dogs to hug/cuddle is best translated in canine body language as "hey don't mess with me or I'll kick your little behind" - probably not the message you were intending! [sm=lol.gif] In general, the further from the top of the dog's head, the less confrontational the gesture... so they like to be touched under the chin, behind the ears, with a belly rub (sometimes), and often most especially with a good butt rub. []
 
If your dog is too territorial on the couch, you might want to rethink his furniture priveleges.
 
 

My JJ was a grouch with everyone but DH and I and even to this day he doesn#%92t like anyone other than us going towards his face…he will snarl at them. Some dogs are sensitive to that. If it does appear that the dog is guarding the couch, then I agree that the couch privileges need to go![]

  As far as the cat thing…we nip that chasing thing as soon as we see that type of behavior in our house.  With greyhounds being prey driven, it could turn into a tragedy very quickly. I am not saying it is that way with Trinity, but if it were me I would rather be safe than sorry!

  I think your obedience class ideas are a good one!  []

Start him in NILIF - Nothing In Life Is Free - immediately.  Revoke his furniture privileges until he can respect that YOU are in control of ALL resources. 
 
What NILIF means is that your dog has to earn everything he gets.  Dinner, treats, trips outside, walks, petting, everything.  You make him sit or perform SOME task until you give him what he wants.  Until he stops this behavior, you are not your dog's "friend" - you need to be his "master".   Do not allow him on the furniture at all, period, for at least several weeks until he has mastered the NILIF trainig and even then make sure he has to DO something to get that reward.  If the behavior resumes, then do not ever allow him on the furniture again. 
 
Having been through this with a dog I eventually had to put down, I would suggest that you take a VERY firm tack with this behavior and DO NOT put up with it.  Get yourself with a behaviorist ASAP, and I mean run!  Every day that your dog is allowed to get by with that behavior, he learns that it works and it will be harder and harder for you to break him of it.  Do it not just for you but for your dog's life.  What if a small child wanted to hug your "nice doggy" while he was laying on the couch?